sphinx.addnodesdocument)}( rawsourcechildren](docutils.nodestarget)}(h.. _9-2:h]
attributes}(ids]classes]names]dupnames]backrefs]refidid1utagnameh
lineKparenthhhsource./Users/john/Documents/SCALE-test/docs/NEWT.rstubh section)}(hhh](h title)}(hmNEWT: A New Transport Algorithm for Two-Dimensional Discrete-Ordinates Analysis in Non-Orthogonal Geometriesh]h TextmNEWT: A New Transport Algorithm for Two-Dimensional Discrete-Ordinates Analysis in Non-Orthogonal Geometries}(hh,h h*hhh!NhNubah}(h]h]h]h]h]uhh(h h%hhh!h"hKubh enumerated_list)}(hhh]h list_item)}(hA. Jessee, M. D. DeHart [1]_
h]h;)}(hhh]h@)}(hJessee, M. D. DeHart [1]_
h]h paragraph)}(hJessee, M. D. DeHart [1]_h](h/Jessee, M. D. DeHart }(hJessee, M. D. DeHart h hNubh footnote_reference)}(h[1]_h]h/1}(hhh hYubah}(h]id2ah]h]h]h]hid158docnameNEWTuhhWh hNresolvedKubeh}(h]h]h]h]h]uhhLh!h"hKh hHubah}(h]h]h]h]h]uhh?h hEubah}(h]h]h]h]h]enumtype
upperalphaprefixhsuffix.uhh:h hAubah}(h]h]h]h]h]uhh?h huhj(h!h"hKh jhhj}j}j*j!subhM)}(hwhereh]h/where}(hjBh j@hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hKh jhhubjP)}(hhh]hM)}(hX:math:`\sigma_{s}\left(\mathbf{r}, \Omega^{\prime} \rightarrow \Omega, E^{\prime} \rightarrow E\right)`≡ macroscopic scattering cross section at position **r** from initial energy
E′ and direction :math:`\Omega`′ to final energy E and direction :math:`\Omega`,h](jY)}(h:math:`\sigma_{s}\left(\mathbf{r}, \Omega^{\prime} \rightarrow \Omega, E^{\prime} \rightarrow E\right)`≡ macroscopic scattering cross section at position **r** from initial energy
E′ and direction :math:`h]h/_\sigma_{s}\left(\mathbf{r}, \Omega^{\prime} \rightarrow \Omega, E^{\prime} \rightarrow E\right)}(hhh jUubah}(h]h]h]h]h]uhjXh jQubh/+Omega`′ to final energy E and direction }(h+\Omega`′ to final energy E and direction h jQubjY)}(h:math:`\Omega`h]h/\Omega}(hhh jhubah}(h]h]h]h]h]uhjXh jQubh/,}(h,h jQubeh}(h]h]h]h]h]uhhLh!h"hKh jNubah}(h]h]h]h]h]uhjOh jhhh!h"hNubh;)}(hhh]h@)}(ha fission source,
h]hM)}(ha fission source,h]h/a fission source,}(hjh jubah}(h]h]h]h]h]uhhLh!h"hKh jubah}(h]h]h]h]h]uhh?h jhhh!h"hNubah}(h]h]h]h]h]h~j hhhhhKuhh:h jhhh!h"hKubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-3uhh
h jhhh!h"hNubj))}(hF(\mathbf{r}, \Omega, E)=\chi(\mathbf{r}, E) \int_{0}^{\infty} d E^{\prime} v\left(\mathbf{r}, E^{\prime}\right) \sigma_{f}\left(\mathbf{r}, E^{\prime}\right) \psi\left(\mathbf{r}, \Omega, E^{\prime}\right) ,h]h/F(\mathbf{r}, \Omega, E)=\chi(\mathbf{r}, E) \int_{0}^{\infty} d E^{\prime} v\left(\mathbf{r}, E^{\prime}\right) \sigma_{f}\left(\mathbf{r}, E^{\prime}\right) \psi\left(\mathbf{r}, \Omega, E^{\prime}\right) ,}(hhh jubah}(h]jah]h]h]h]docnamehjnumberKlabeleq9-2-3nowrapj=j>uhj(h!h"hKh jhhj}j}jjsubhM)}(hwhereh]h/where}(hjh jhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hKh jhhubjP)}(hhh](hM)}(h:math:`\sigma_{f}\left(\mathbf{r}, E^{\prime}\right)` ≡ macroscopic fission cross section at position **r** and energy E′ (assumed
to be isotropic),h](jY)}(h5:math:`\sigma_{f}\left(\mathbf{r}, E^{\prime}\right)`h]h/-\sigma_{f}\left(\mathbf{r}, E^{\prime}\right)}(hhh jubah}(h]h]h]h]h]uhjXh jubh/4 ≡ macroscopic fission cross section at position }(h4 ≡ macroscopic fission cross section at position h jubh)}(h**r**h]h/r}(hhh jubah}(h]h]h]h]h]uhhh jubh/+ and energy E′ (assumed
to be isotropic),}(h+ and energy E′ (assumed
to be isotropic),h jubeh}(h]h]h]h]h]uhhLh!h"hKh jubhM)}(h:math:`v\left(\mathbf{r}, E^{\prime}\right)` ≡ number of neutrons released per fission event at position **r** and
energy E′,h](jY)}(h,:math:`v\left(\mathbf{r}, E^{\prime}\right)`h]h/$v\left(\mathbf{r}, E^{\prime}\right)}(hhh jubah}(h]h]h]h]h]uhjXh jubh/? ≡ number of neutrons released per fission event at position }(h? ≡ number of neutrons released per fission event at position h jubh)}(h**r**h]h/r}(hhh jubah}(h]h]h]h]h]uhhh jubh/ and
energy E′,}(h and
energy E′,h jubeh}(h]h]h]h]h]uhhLh!h"hMh jubhM)}(h`:math:`\chi(\mathbf{r}, E)` ≡ fraction of neutrons that are born at **r** and at energy E, andh](jY)}(h:math:`\chi(\mathbf{r}, E)`h]h/\chi(\mathbf{r}, E)}(hhh j<ubah}(h]h]h]h]h]uhjXh j8ubh/+ ≡ fraction of neutrons that are born at }(h+ ≡ fraction of neutrons that are born at h j8ubh)}(h**r**h]h/r}(hhh jOubah}(h]h]h]h]h]uhhh j8ubh/ and at energy E, and}(h and at energy E, andh j8ubeh}(h]h]h]h]h]uhhLh!h"hMh jubeh}(h]h]h]h]h]uhjOh jhhh!h"hNubh;)}(hhh]h@)}(h*an external or fixed source, S(**r** ,E).
h]hM)}(h)an external or fixed source, S(**r** ,E).h](h/an external or fixed source, S(}(han external or fixed source, S(h juubh)}(h**r**h]h/r}(hhh j~ubah}(h]h]h]h]h]uhhh juubh/ ,E).}(h ,E).h juubeh}(h]h]h]h]h]uhhLh!h"hMh jqubah}(h]h]h]h]h]uhh?h jnhhh!h"hNubah}(h]h]h]h]h]h~j hhhhhKuhh:h jhhh!h"hMubhM)}(hXIn general, the transport equation can be difficult to apply and can be
solved analytically only for highly idealized cases. Hence,
simplifications and numerical approximations are often necessary to
apply the equation in engineering applications. Traditional
discrete-ordinates methods are based on a finite-difference
approximation to solve the flux streaming (leakage) term. Such
differencing schemes are intimately tied to the coordinate system in
which the differencing equations are developed, and it becomes difficult
to represent non-orthogonal volumes within that coordinate system. For
example, it is not possible to exactly represent a cylinder in a 2-D
Cartesian coordinate system; one must approximate the cylinder with a
number of rectangular cells. A close approximation can require a large
number of computational cells. However, the ESC approach for
discretizing computational cells allows the use of non-orthogonal
computational cells composed of arbitrary polygons. Using this method,
practically any shape can be represented within a Cartesian grid to a
very close approximation. The ESC approach is discussed in the following
sections.h]h/XIn general, the transport equation can be difficult to apply and can be
solved analytically only for highly idealized cases. Hence,
simplifications and numerical approximations are often necessary to
apply the equation in engineering applications. Traditional
discrete-ordinates methods are based on a finite-difference
approximation to solve the flux streaming (leakage) term. Such
differencing schemes are intimately tied to the coordinate system in
which the differencing equations are developed, and it becomes difficult
to represent non-orthogonal volumes within that coordinate system. For
example, it is not possible to exactly represent a cylinder in a 2-D
Cartesian coordinate system; one must approximate the cylinder with a
number of rectangular cells. A close approximation can require a large
number of computational cells. However, the ESC approach for
discretizing computational cells allows the use of non-orthogonal
computational cells composed of arbitrary polygons. Using this method,
practically any shape can be represented within a Cartesian grid to a
very close approximation. The ESC approach is discussed in the following
sections.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jhhubh)}(h.. _9-2-2-2:h]h}(h]h]h]h]h]hid13uhh
hMh jhhh!h"ubeh}(h](boltzmann-transport-equationjeh]h](boltzmann transport equation9-2-2-1eh]h]uhh#h jhhh!h"hKj}jjsj}jjsubh$)}(hhh](h))}(h%The step characteristic approximationh]h/%The step characteristic approximation}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hMubhM)}(hXEfficient application of discrete-ordinates methods is difficult when
dealing with complicated non-orthogonal geometries because of the nature
of finite difference approximations for spatial derivatives. An
alternative to the discrete representation of the spatial variable is
achieved in the method of characteristics, in which the transport
equation is solved analytically along characteristic directions within a
computational cell. The angular flux is solved along the *s*-axis,
where this axis is oriented along the characteristic direction :math:`\Omega`. Since
only the angular flux in direction :math:`\Omega` is of concern, then the streaming
term can be rewritten ash](h/XEfficient application of discrete-ordinates methods is difficult when
dealing with complicated non-orthogonal geometries because of the nature
of finite difference approximations for spatial derivatives. An
alternative to the discrete representation of the spatial variable is
achieved in the method of characteristics, in which the transport
equation is solved analytically along characteristic directions within a
computational cell. The angular flux is solved along the }(hXEfficient application of discrete-ordinates methods is difficult when
dealing with complicated non-orthogonal geometries because of the nature
of finite difference approximations for spatial derivatives. An
alternative to the discrete representation of the spatial variable is
achieved in the method of characteristics, in which the transport
equation is solved analytically along characteristic directions within a
computational cell. The angular flux is solved along the h jhhh!NhNubj)}(h*s*h]h/s}(hhh jubah}(h]h]h]h]h]uhjh jubh/F-axis,
where this axis is oriented along the characteristic direction }(hF-axis,
where this axis is oriented along the characteristic direction h jhhh!NhNubjY)}(h:math:`\Omega`h]h/\Omega}(hhh jubah}(h]h]h]h]h]uhjXh jubh/,. Since
only the angular flux in direction }(h,. Since
only the angular flux in direction h jhhh!NhNubjY)}(h:math:`\Omega`h]h/\Omega}(hhh jubah}(h]h]h]h]h]uhjXh jubh/; is of concern, then the streaming
term can be rewritten as}(h; is of concern, then the streaming
term can be rewritten ash jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM h jhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-4uhh
h jhhh!h"hNubj))}(hJ\Omega \cdot \nabla \psi(\mathbf{r}, \Omega, E)=\frac{d \psi(s, E)}{d s} .h]h/J\Omega \cdot \nabla \psi(\mathbf{r}, \Omega, E)=\frac{d \psi(s, E)}{d s} .}(hhh j*ubah}(h]j)ah]h]h]h]docnamehjnumberKlabeleq9-2-4nowrapj=j>uhj(h!h"hM+h jhhj}j}j)j subhM)}(h\Hence :eq:`eq9-2-1` can be written in the characteristic form (omitting *E* for
clarity) ash](h/Hence }(hHence h j?hhh!NhNubj)}(h
:eq:`eq9-2-1`h]h literal)}(hjJh]h/eq9-2-1}(hhh jNubah}(h]h](jEeqeh]h]h]uhjLh jHubah}(h]h]h]h]h]refdochj refdomainjXreftypejXrefexplicitrefwarnjWeq9-2-1uhjh!h"hM0h j?ubh/6 can be written in the characteristic form (omitting }(h6 can be written in the characteristic form (omitting h j?hhh!NhNubj)}(h*E*h]h/E}(hhh jmubah}(h]h]h]h]h]uhjh j?ubh/ for
clarity) as}(h for
clarity) ash j?hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM0h jhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-5uhh
h jhhh!h"hNubj))}(h;\frac{d \psi(s)}{d s}+\sigma_{t}(s) \psi(\mathrm{s})=Q(s) ,h]h/;\frac{d \psi(s)}{d s}+\sigma_{t}(s) \psi(\mathrm{s})=Q(s) ,}(hhh jubah}(h]jah]h]h]h]docnamehjnumberKlabeleq9-2-5nowrapj=j>uhj(h!h"hM3h jhhj}j}jjsubhM)}(hAwhich has a solution of the form :cite:`hildebrand_advanced_1976`h](h/!which has a solution of the form }(h!which has a solution of the form h jhhh!NhNubj)}(hhildebrand_advanced_1976h]j)}(hjh]h/[hildebrand_advanced_1976]}(hhh jubah}(h]h]h]h]h]uhjh jubah}(h]id14ah]jah]h]h] refdomainjreftypej reftargetjrefwarnsupport_smartquotesuhjh!h"hM8h jhhubeh}(h]h]h]h]h]uhhLh!h"hM8h jhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-6uhh
h jhhh!h"hNubj))}(hl\psi(s)=\psi_{0} e^{-\sigma_{t} s}+e^{-\sigma_{t} s} \int_{0}^{s} Q e^{\sigma_{t} s^{\prime}} d s^{\prime} ,h]h/l\psi(s)=\psi_{0} e^{-\sigma_{t} s}+e^{-\sigma_{t} s} \int_{0}^{s} Q e^{\sigma_{t} s^{\prime}} d s^{\prime} ,}(hhh jubah}(h]jah]h]h]h]docnamehjnumberKlabeleq9-2-6nowrapj=j>uhj(h!h"hM:h jhhj}j}jjsubhM)}(hXwhere s is the distance along the characteristic direction :math:`\Omega`, and
ψ\ :sub:`0` is the known angular flux at *s*\ =0. The value for
ψ\ :sub:`0` is given from boundary conditions for known cell sides, and
angular fluxes on unknown sides are computed using Eq. (9.2.6). Methods
for the determination of an appropriate value for ψ\ :sub:`0` and for
evaluation of the integral term vary in different solution
techniques.\ :sup:`4–9`\ :cite:`lewis_j_nodate,hildebrand_advanced_1976,alcouffe_review_1981,lathrop_spatial_1969,alcouffe_computational_1979,larsen_linear_1981,lathrop_spatial_1968`.
One of the simplest schemes employing the Method of Characteristics is
the Step Characteristic (SC) method developed by Lathrop :cite:`alcouffe_review_1981`. In
this approach, the source Q and macroscopic total cross section σt are
assumed to be constant within a computational cell and the angular flux
is assumed constant on the cell boundaries of incoming direction.
Integration of Eq. :eq:`eq9-2-6` can be performed to obtainh](h/;where s is the distance along the characteristic direction }(h;where s is the distance along the characteristic direction h jhhh!NhNubjY)}(h:math:`\Omega`h]h/\Omega}(hhh jubah}(h]h]h]h]h]uhjXh jubh/
, and
ψ }(h
, and
ψ\ h jhhh!NhNubj)}(h:sub:`0`h]h/0}(hhh jubah}(h]h]h]h]h]uhjh jubh/ is the known angular flux at }(h is the known angular flux at h jhhh!NhNubj)}(h*s*h]h/s}(hhh jubah}(h]h]h]h]h]uhjh jubh/ =0. The value for
ψ }(h\ =0. The value for
ψ\ h jhhh!NhNubj)}(h:sub:`0`h]h/0}(hhh j2ubah}(h]h]h]h]h]uhjh jubh/ is given from boundary conditions for known cell sides, and
angular fluxes on unknown sides are computed using Eq. (9.2.6). Methods
for the determination of an appropriate value for ψ }(h is given from boundary conditions for known cell sides, and
angular fluxes on unknown sides are computed using Eq. (9.2.6). Methods
for the determination of an appropriate value for ψ\ h jhhh!NhNubj)}(h:sub:`0`h]h/0}(hhh jEubah}(h]h]h]h]h]uhjh jubh/Q and for
evaluation of the integral term vary in different solution
techniques. }(hQ and for
evaluation of the integral term vary in different solution
techniques.\ h jhhh!NhNubh superscript)}(h:sup:`4–9`h]h/4–9}(hhh jZubah}(h]h]h]h]h]uhjXh jubh/ }(h\ h jhhh!NhNubj)}(hlewis_j_nodateh]j)}(hjoh]h/[lewis_j_nodate]}(hhh jqubah}(h]h]h]h]h]uhjh jmubah}(h]id15ah]jah]h]h] refdomainjreftypej reftargetjorefwarnsupport_smartquotesuhjh!h"hM?h jhhubj)}(hhildebrand_advanced_1976h]j)}(hjh]h/[hildebrand_advanced_1976]}(hhh jubah}(h]h]h]h]h]uhjh jubah}(h]id16ah]jah]h]h] refdomainjreftypej reftargetjrefwarnsupport_smartquotesuhjh!h"hM?h jhhubj)}(halcouffe_review_1981h]j)}(hjh]h/[alcouffe_review_1981]}(hhh jubah}(h]h]h]h]h]uhjh jubah}(h]id17ah]jah]h]h] refdomainjreftypej reftargetjrefwarnsupport_smartquotesuhjh!h"hM?h jhhubj)}(hlathrop_spatial_1969h]j)}(hjh]h/[lathrop_spatial_1969]}(hhh jubah}(h]h]h]h]h]uhjh jubah}(h]id18ah]jah]h]h] refdomainjreftypej reftargetjrefwarnsupport_smartquotesuhjh!h"hM?h jhhubj)}(halcouffe_computational_1979h]j)}(hjh]h/[alcouffe_computational_1979]}(hhh jubah}(h]h]h]h]h]uhjh jubah}(h]id19ah]jah]h]h] refdomainjreftypej reftargetjrefwarnsupport_smartquotesuhjh!h"hM?h jhhubj)}(hlarsen_linear_1981h]j)}(hj h]h/[larsen_linear_1981]}(hhh j ubah}(h]h]h]h]h]uhjh jubah}(h]id20ah]jah]h]h] refdomainjreftypej reftargetj refwarnsupport_smartquotesuhjh!h"hM?h jhhubj)}(hlathrop_spatial_1968h]j)}(hj h]h/[lathrop_spatial_1968]}(hhh j ubah}(h]h]h]h]h]uhjh j ubah}(h]id21ah]jah]h]h] refdomainjreftypej reftargetj refwarnsupport_smartquotesuhjh!h"hM?h jhhubh/.
One of the simplest schemes employing the Method of Characteristics is
the Step Characteristic (SC) method developed by Lathrop }(h.
One of the simplest schemes employing the Method of Characteristics is
the Step Characteristic (SC) method developed by Lathrop h jhhh!NhNubj)}(halcouffe_review_1981h]j)}(hj? h]h/[alcouffe_review_1981]}(hhh jA ubah}(h]h]h]h]h]uhjh j= ubah}(h]id22ah]jah]h]h] refdomainjreftypej reftargetj? refwarnsupport_smartquotesuhjh!h"hM?h jhhubh/. In
this approach, the source Q and macroscopic total cross section σt are
assumed to be constant within a computational cell and the angular flux
is assumed constant on the cell boundaries of incoming direction.
Integration of Eq. }(h. In
this approach, the source Q and macroscopic total cross section σt are
assumed to be constant within a computational cell and the angular flux
is assumed constant on the cell boundaries of incoming direction.
Integration of Eq. h jhhh!NhNubj)}(h
:eq:`eq9-2-6`h]jM)}(hja h]h/eq9-2-6}(hhh jc ubah}(h]h](jEeqeh]h]h]uhjLh j_ ubah}(h]h]h]h]h]refdochj refdomainjXreftypejm refexplicitrefwarnjWeq9-2-6uhjh!h"hM?h jubh/ can be performed to obtain}(h can be performed to obtainh jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM?h jhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-7uhh
h jhhh!h"hNubj))}(hY\psi(s)=\psi_{0} e^{-\sigma_{t} s}+\frac{Q}{\sigma_{t}}\left(1-e^{-\sigma_{t} s}\right) .h]h/Y\psi(s)=\psi_{0} e^{-\sigma_{t} s}+\frac{Q}{\sigma_{t}}\left(1-e^{-\sigma_{t} s}\right) .}(hhh j ubah}(h]j ah]h]h]h]docnamehjnumberKlabeleq9-2-7nowrapj=j>uhj(h!h"hMMh jhhj}j}j j subhM)}(hX!:numref:`fig9-2-1` shows a sample computational cell in which the SC method
can be applied. For a given characteristic direction :math:`\Omega`, the angular flux
on any unknown side may be expressed in terms of a suitable average of
fluxes from known sides, which contribute to the unknown side. For the
characteristic direction :math:`\Omega` shown in :numref:`fig9-2-1`, the unknown “top” flux
ψ\ :sub:`T` may be computed as a linearly weighted average of
contributions from known sides ψ\ :sub:`B` and ψ\ :sub:`L`. The fluxes
on each of the two known sides are taken to be constant along the length
of each side, representing the average angular flux in direction :math:`\Omega` and
must be specified from external boundary conditions or from a completed
calculation in an adjacent cell.h](j)}(h:numref:`fig9-2-1`h]jM)}(hj h]h/fig9-2-1}(hhh j ubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh j ubah}(h]h]h]h]h]refdochj refdomainj reftypenumrefrefexplicitrefwarnjWfig9-2-1uhjh!h"hMRh j ubh/p shows a sample computational cell in which the SC method
can be applied. For a given characteristic direction }(hp shows a sample computational cell in which the SC method
can be applied. For a given characteristic direction h j hhh!NhNubjY)}(h:math:`\Omega`h]h/\Omega}(hhh j ubah}(h]h]h]h]h]uhjXh j ubh/, the angular flux
on any unknown side may be expressed in terms of a suitable average of
fluxes from known sides, which contribute to the unknown side. For the
characteristic direction }(h, the angular flux
on any unknown side may be expressed in terms of a suitable average of
fluxes from known sides, which contribute to the unknown side. For the
characteristic direction h j hhh!NhNubjY)}(h:math:`\Omega`h]h/\Omega}(hhh j ubah}(h]h]h]h]h]uhjXh j ubh/
shown in }(h
shown in h j hhh!NhNubj)}(h:numref:`fig9-2-1`h]jM)}(hj h]h/fig9-2-1}(hhh j ubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh j ubah}(h]h]h]h]h]refdochj refdomainj
reftypenumrefrefexplicitrefwarnjWfig9-2-1uhjh!h"hMRh j ubh/!, the unknown “top” flux
ψ }(h!, the unknown “top” flux
ψ\ h j hhh!NhNubj)}(h:sub:`T`h]h/T}(hhh j
ubah}(h]h]h]h]h]uhjh j ubh/W may be computed as a linearly weighted average of
contributions from known sides ψ }(hW may be computed as a linearly weighted average of
contributions from known sides ψ\ h j hhh!NhNubj)}(h:sub:`B`h]h/B}(hhh j.
ubah}(h]h]h]h]h]uhjh j ubh/ and ψ }(h and ψ\ h j hhh!NhNubj)}(h:sub:`L`h]h/L}(hhh jA
ubah}(h]h]h]h]h]uhjh j ubh/. The fluxes
on each of the two known sides are taken to be constant along the length
of each side, representing the average angular flux in direction }(h. The fluxes
on each of the two known sides are taken to be constant along the length
of each side, representing the average angular flux in direction h j hhh!NhNubjY)}(h:math:`\Omega`h]h/\Omega}(hhh jT
ubah}(h]h]h]h]h]uhjXh j ubh/n and
must be specified from external boundary conditions or from a completed
calculation in an adjacent cell.}(hn and
must be specified from external boundary conditions or from a completed
calculation in an adjacent cell.h j hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMRh jhhubhM)}(hXThe set of characteristic directions is chosen from a quadrature set, so
that the resulting angular fluxes may be numerically integrated to
obtain a scalar flux. Knowing the lengths of the sides of a rectangular
cell (∆x and ∆y) and the direction cosines of :math:`\Omega` in the *x-y* plane
(μ and η), a function for the length *s* can easily be determined. The
solution for from Eq. :eq:`eq9-2-7` can then be integrated along the length of
each unknown side to determine the average angular flux of the unknown
side. Once the angular flux is known on all four sides, a neutron
balance on the cell can be used to determine the cell’s average angular
flux.h](h/XThe set of characteristic directions is chosen from a quadrature set, so
that the resulting angular fluxes may be numerically integrated to
obtain a scalar flux. Knowing the lengths of the sides of a rectangular
cell (∆x and ∆y) and the direction cosines of }(hXThe set of characteristic directions is chosen from a quadrature set, so
that the resulting angular fluxes may be numerically integrated to
obtain a scalar flux. Knowing the lengths of the sides of a rectangular
cell (∆x and ∆y) and the direction cosines of h jm
hhh!NhNubjY)}(h:math:`\Omega`h]h/\Omega}(hhh jv
ubah}(h]h]h]h]h]uhjXh jm
ubh/ in the }(h in the h jm
hhh!NhNubj)}(h*x-y*h]h/x-y}(hhh j
ubah}(h]h]h]h]h]uhjh jm
ubh/0 plane
(μ and η), a function for the length }(h0 plane
(μ and η), a function for the length h jm
hhh!NhNubj)}(h*s*h]h/s}(hhh j
ubah}(h]h]h]h]h]uhjh jm
ubh/6 can easily be determined. The
solution for from Eq. }(h6 can easily be determined. The
solution for from Eq. /h jm
hhh!NhNubj)}(h
:eq:`eq9-2-7`h]jM)}(hj
h]h/eq9-2-7}(hhh j
ubah}(h]h](jEeqeh]h]h]uhjLh j
ubah}(h]h]h]h]h]refdochj refdomainjXreftypej
refexplicitrefwarnjWeq9-2-7uhjh!h"hM^h jm
ubh/X can then be integrated along the length of
each unknown side to determine the average angular flux of the unknown
side. Once the angular flux is known on all four sides, a neutron
balance on the cell can be used to determine the cell’s average angular
flux.}(hX can then be integrated along the length of
each unknown side to determine the average angular flux of the unknown
side. Once the angular flux is known on all four sides, a neutron
balance on the cell can be used to determine the cell’s average angular
flux.h jm
hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM^h jhhubhM)}(hX Although the SC method described above is based on rectangular cells,
the derivation of Eq. :eq:`eq9-2-7` makes no assumptions about the shape of
the cell. It merely requires knowledge of the relationship between cell
edges along the direction of the characteristic. Hence, the method is
not restricted to any particular geometry. Because it is an extension of
the SC approach into generalized cells, the method developed here for
generalized geometries is referred to as the Extended Step
Characteristic (ESC) method.h](h/^Although the SC method described above is based on rectangular cells,
the derivation of Eq. }(h^Although the SC method described above is based on rectangular cells,
the derivation of Eq. h j
hhh!NhNubj)}(h
:eq:`eq9-2-7`h]jM)}(hj
h]h/eq9-2-7}(hhh j
ubah}(h]h](jEeqeh]h]h]uhjLh j
ubah}(h]h]h]h]h]refdochj refdomainjXreftypej
refexplicitrefwarnjWeq9-2-7uhjh!h"hMih j
ubh/X makes no assumptions about the shape of
the cell. It merely requires knowledge of the relationship between cell
edges along the direction of the characteristic. Hence, the method is
not restricted to any particular geometry. Because it is an extension of
the SC approach into generalized cells, the method developed here for
generalized geometries is referred to as the Extended Step
Characteristic (ESC) method.}(hX makes no assumptions about the shape of
the cell. It merely requires knowledge of the relationship between cell
edges along the direction of the characteristic. Hence, the method is
not restricted to any particular geometry. Because it is an extension of
the SC approach into generalized cells, the method developed here for
generalized geometries is referred to as the Extended Step
Characteristic (ESC) method.h j
hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMih jhhubh)}(h
.. _fig9-2-1:h]h}(h]h]h]h]h]hfig9-2-1uhh
hMrh jhhh!h"ubh figure)}(hhh](h image)}(h.. figure:: figs/NEWT/fig1.png
:align: center
:width: 400
Typical rectangular cell used in the step characteristic approach.
h]h}(h]h]h]h]h]width400urifigs/NEWT/fig1.png
candidates}*j)suhjh jh!h"hMwubh caption)}(hBTypical rectangular cell used in the step characteristic approach.h]h/BTypical rectangular cell used in the step characteristic approach.}(hj1h j/ubah}(h]h]h]h]h]uhj-h!h"hMwh jubeh}(h](id159jeh]h]fig9-2-1ah]h]aligncenteruhjhMwh jhhh!h"j}jBj
sj}jj
subh)}(h.. _9-2-2-3:h]h}(h]h]h]h]h]hid23uhh
hMyh jhhh!h"ubeh}(h](%the-step-characteristic-approximationjeh]h](%the step characteristic approximation9-2-2-2eh]h]uhh#h jhhh!h"hMj}jZjsj}jjsubh$)}(hhh](h))}(h)The Extended Step Characteristic approachh]h/)The Extended Step Characteristic approach}(hjdh jbhhh!NhNubah}(h]h]h]h]h]uhh(h j_hhh!h"hM|ubhM)}(hXiThe theory of the ESC approach is developed and explained in detail in
:cite:`dehart_discrete_1992`. However, the work has evolved significantly from that time, most
notably in the elimination of a requirement for non-reentrant polygons
(convex). The following subsections describe the primary equations
applied in the ESC approach as currently applied in NEWT.h](h/GThe theory of the ESC approach is developed and explained in detail in
}(hGThe theory of the ESC approach is developed and explained in detail in
h jphhh!NhNubj)}(hdehart_discrete_1992h]j)}(hj{h]h/[dehart_discrete_1992]}(hhh j}ubah}(h]h]h]h]h]uhjh jyubah}(h]id24ah]jah]h]h] refdomainjreftypej reftargetj{refwarnsupport_smartquotesuhjh!h"hM~h jphhubh/X. However, the work has evolved significantly from that time, most
notably in the elimination of a requirement for non-reentrant polygons
(convex). The following subsections describe the primary equations
applied in the ESC approach as currently applied in NEWT.}(hX. However, the work has evolved significantly from that time, most
notably in the elimination of a requirement for non-reentrant polygons
(convex). The following subsections describe the primary equations
applied in the ESC approach as currently applied in NEWT.h jphhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM~h j_hhubh)}(h.. _9-2-2-3-1:h]h}(h]h]h]h]h]hid25uhh
hMh j_hhh!h"ubh$)}(hhh](h))}(hCell properties and geometriesh]h/Cell properties and geometries}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hMubhM)}(hX{The two primary assumptions of the ESC method are that (1) within each
computational cell all properties (i.e., σt and Q) are uniform and
(2) cell boundaries are defined by straight lines. The restriction of a
computational cell to boundaries consisting of a set of straight lines
results in computational cells that are limited to polygons. However, as
will be seen later, no restrictions are placed on the shape of the
polygon or on the number of sides in the polygon. However, the size of
the polygon will be limited. In practical applications, properties are
unlikely to remain constant over significant volumes. Thus this
approach, like many other differencing schemes, is a poor approximation
when cell volumes become too large. Although σt is a material property
and may remain spatially constant, the source term Q, which depends on
the neutron flux, will vary with position. However, since the solution
would become exact in an infinitesimally small cell, it is expected that
the approximation will be reasonable for computational cells in which
the change in the flux (and therefore the source) is small over the
domain of the cell.h]h/X{The two primary assumptions of the ESC method are that (1) within each
computational cell all properties (i.e., σt and Q) are uniform and
(2) cell boundaries are defined by straight lines. The restriction of a
computational cell to boundaries consisting of a set of straight lines
results in computational cells that are limited to polygons. However, as
will be seen later, no restrictions are placed on the shape of the
polygon or on the number of sides in the polygon. However, the size of
the polygon will be limited. In practical applications, properties are
unlikely to remain constant over significant volumes. Thus this
approach, like many other differencing schemes, is a poor approximation
when cell volumes become too large. Although σt is a material property
and may remain spatially constant, the source term Q, which depends on
the neutron flux, will vary with position. However, since the solution
would become exact in an infinitesimally small cell, it is expected that
the approximation will be reasonable for computational cells in which
the change in the flux (and therefore the source) is small over the
domain of the cell.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jhhubhM)}(hX
As a result of this geometric configuration, each side of a cell can
have one of three possible attributes relative to particle flow in a
given characteristic direction, as illustrated in :numref:`fig9-2-2`: (1) flow
can enter the cell when crossing a side (as shown by sides E and F in
the figure); (2) flow can exit the cell when crossing a side (sides B
and C); or (3) in a special case, flow may be parallel to the
orientation of a given side (sides A and D). Expressed mathematically,
these relationships becomeh](h/As a result of this geometric configuration, each side of a cell can
have one of three possible attributes relative to particle flow in a
given characteristic direction, as illustrated in }(hAs a result of this geometric configuration, each side of a cell can
have one of three possible attributes relative to particle flow in a
given characteristic direction, as illustrated in h jhhh!NhNubj)}(h:numref:`fig9-2-2`h]jM)}(hjh]h/fig9-2-2}(hhh jubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjreftypenumrefrefexplicitrefwarnjWfig9-2-2uhjh!h"hMh jubh/X<: (1) flow
can enter the cell when crossing a side (as shown by sides E and F in
the figure); (2) flow can exit the cell when crossing a side (sides B
and C); or (3) in a special case, flow may be parallel to the
orientation of a given side (sides A and D). Expressed mathematically,
these relationships become}(hX<: (1) flow
can enter the cell when crossing a side (as shown by sides E and F in
the figure); (2) flow can exit the cell when crossing a side (sides B
and C); or (3) in a special case, flow may be parallel to the
orientation of a given side (sides A and D). Expressed mathematically,
these relationships becomeh jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-8uhh
h jhhh!h"hNubj))}(h4\text { Category } 1: \Omega_{k} \cdot \hat{n}_{i}<0h]h/4\text { Category } 1: \Omega_{k} \cdot \hat{n}_{i}<0}(hhh j ubah}(h]jah]h]h]h]docnamehjnumberKlabeleq9-2-8nowrapj=j>uhj(h!h"hMh jhhj}j}jjsubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-9uhh
h jhhh!h"hNubj))}(h4\text { Category } 2: \Omega_{k} \cdot \hat{n}_{i}>0h]h/4\text { Category } 2: \Omega_{k} \cdot \hat{n}_{i}>0}(hhh j(ubah}(h]j'ah]h]h]h]docnamehjnumberK labeleq9-2-9nowrapj=j>uhj(h!h"hMh jhhj}j}j'jsubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-10uhh
h jhhh!h"hNubj))}(h4\text { Category } 1: \Omega_{k} \cdot \hat{n}_{i}=0h]h/4\text { Category } 1: \Omega_{k} \cdot \hat{n}_{i}=0}(hhh jGubah}(h]jFah]h]h]h]docnamehjnumberK
labeleq9-2-10nowrapj=j>uhj(h!h"hMh jhhj}j}jFj=subhM)}(hX'where :math:`\hat{n}_{i}` is a unit vector in the cell-outward direction normal to
side \ *i*, and :math:`\Omega_{k}` is the *k*\ :sup:`th` discrete element of a set of
characteristic directions. A category 1 side will be termed an
“incoming” side with respect to the direction :math:`\Omega_{k}`, and a category 2 side
will be referred to as an “outgoing” side. For simplicity, the
definition of Eq. :eq:`eq9-2-10` will be included as a special case of
Eq. :eq:`eq9-2-8` for an incoming side. Thus, Eq. :eq:`eq9-2-8` can be rewritten ash](h/where }(hwhere h j\hhh!NhNubjY)}(h:math:`\hat{n}_{i}`h]h/\hat{n}_{i}}(hhh jeubah}(h]h]h]h]h]uhjXh j\ubh/B is a unit vector in the cell-outward direction normal to
side }(hB is a unit vector in the cell-outward direction normal to
side \ h j\hhh!NhNubj)}(h*i*h]h/i}(hhh jxubah}(h]h]h]h]h]uhjh j\ubh/, and }(h, and h j\hhh!NhNubjY)}(h:math:`\Omega_{k}`h]h/
\Omega_{k}}(hhh jubah}(h]h]h]h]h]uhjXh j\ubh/ is the }(h is the h j\hhh!NhNubj)}(h*k*h]h/k}(hhh jubah}(h]h]h]h]h]uhjh j\ubh/ }(h\ h j\hhh!NhNubjY)}(h :sup:`th`h]h/th}(hhh jubah}(h]h]h]h]h]uhjXh j\ubh/ discrete element of a set of
characteristic directions. A category 1 side will be termed an
“incoming” side with respect to the direction }(h discrete element of a set of
characteristic directions. A category 1 side will be termed an
“incoming” side with respect to the direction h j\hhh!NhNubjY)}(h:math:`\Omega_{k}`h]h/
\Omega_{k}}(hhh jubah}(h]h]h]h]h]uhjXh j\ubh/o, and a category 2 side
will be referred to as an “outgoing” side. For simplicity, the
definition of Eq. }(ho, and a category 2 side
will be referred to as an “outgoing” side. For simplicity, the
definition of Eq. h j\hhh!NhNubj)}(h:eq:`eq9-2-10`h]jM)}(hjh]h/eq9-2-10}(hhh jubah}(h]h](jEeqeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjXreftypejrefexplicitrefwarnjWeq9-2-10uhjh!h"hMh j\ubh/, will be included as a special case of
Eq. }(h, will be included as a special case of
Eq. h j\hhh!NhNubj)}(h
:eq:`eq9-2-8`h]jM)}(hjh]h/eq9-2-8}(hhh jubah}(h]h](jEeqeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjXreftypej
refexplicitrefwarnjWeq9-2-8uhjh!h"hMh j\ubh/" for an incoming side. Thus, Eq. }(h" for an incoming side. Thus, Eq. h j\hhh!NhNubj)}(h
:eq:`eq9-2-8`h]jM)}(hj
h]h/eq9-2-8}(hhh j!
ubah}(h]h](jEeqeh]h]h]uhjLh j
ubah}(h]h]h]h]h]refdochj refdomainjXreftypej+
refexplicitrefwarnjWeq9-2-8uhjh!h"hMh j\ubh/ can be rewritten as}(h can be rewritten ash j\hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-11uhh
h jhhh!h"hNubj))}(hf\text { Side } i \text { is incoming with respect to } \Omega_{k}: \Omega_{k} \cdot \hat{n}_{i} \leq 0h]h/f\text { Side } i \text { is incoming with respect to } \Omega_{k}: \Omega_{k} \cdot \hat{n}_{i} \leq 0}(hhh jP
ubah}(h]jO
ah]h]h]h]docnamehjnumberKlabeleq9-2-11nowrapj=j>uhj(h!h"hMh jhhj}j}jO
jF
subh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-12uhh
h jhhh!h"hNubj))}(ha\text { Side } i \text { is outgoing with respect to } \Omega_{k}: \Omega_{k} \cdot \hat{n}_{i}>0h]h/a\text { Side } i \text { is outgoing with respect to } \Omega_{k}: \Omega_{k} \cdot \hat{n}_{i}>0}(hhh jo
ubah}(h]jn
ah]h]h]h]docnamehjnumberKlabeleq9-2-12nowrapj=j>uhj(h!h"hMh jhhj}j}jn
je
subhM)}(hTo solve for fluxes (flow) on outgoing sides of a cell, one must know fluxes on
all incoming sides. Each incoming side of each cell will be given from a
boundary condition or will be the outgoing side of an adjacent cell.h]h/To solve for fluxes (flow) on outgoing sides of a cell, one must know fluxes on
all incoming sides. Each incoming side of each cell will be given from a
boundary condition or will be the outgoing side of an adjacent cell.}(hj
h j
hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jhhubh)}(h
.. _fig9-2-2:h]h}(h]h]h]h]h]hfig9-2-2uhh
hMh jhhh!h"ubj)}(hhh](j)}(h.. figure:: figs/NEWT/fig2.png
:align: center
:width: 500
Orientation of the sides of a cell with respect to a given direction vector.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig2.pngj*}j,j
suhjh j
h!h"hMubj.)}(hLOrientation of the sides of a cell with respect to a given direction vector.h]h/LOrientation of the sides of a cell with respect to a given direction vector.}(hj
h j
ubah}(h]h]h]h]h]uhj-h!h"hMh j
ubeh}(h](id160j
eh]h]fig9-2-2ah]h]jEcenteruhjhMh jhhh!h"j}j
j
sj}j
j
subh)}(h.. _9-2-2-3-2:h]h}(h]h]h]h]h]hid26uhh
hMh jhhh!h"ubeh}(h](cell-properties-and-geometriesjeh]h](cell properties and geometries 9-2-2-3-1eh]h]uhh#h j_hhh!h"hMj}j
jsj}jjsubh$)}(hhh](h))}(hRelationships between cellsh]h/Relationships between cells}(hj
h j
hhh!NhNubah}(h]h]h]h]h]uhh(h j
hhh!h"hMubhM)}(hXIn the ESC method, the shape of the computational cell and the form of
the neutron balance differ from that used in traditional
discrete-ordinates methods. Nevertheless, the relationships between
cells are treated essentially as they would be in traditional
approaches. The entire problem domain is mapped in terms of a set of
finite cells. Each side of each cell is adjacent to either an external
boundary condition or another cell. For each discrete direction, cells
are swept in a predetermined order beginning at a known boundary (from a
specified external boundary condition) moving in the given direction.
The precise order of sweep is such that as the solution for one cell is
obtained, the cell provides sufficient boundary conditions for the
solution of an adjacent cell. Hence, cells sharing a given side share
the value of the angular flux on that side. Knowledge of the flux on all
incoming sides of a cell is sufficient to solve for all outgoing sides.
Once the angular flux has been determined for all sides of the cell for
the given direction, it is possible to use a neutron balance to compute
the average value of the angular flux within the cell.h]h/XIn the ESC method, the shape of the computational cell and the form of
the neutron balance differ from that used in traditional
discrete-ordinates methods. Nevertheless, the relationships between
cells are treated essentially as they would be in traditional
approaches. The entire problem domain is mapped in terms of a set of
finite cells. Each side of each cell is adjacent to either an external
boundary condition or another cell. For each discrete direction, cells
are swept in a predetermined order beginning at a known boundary (from a
specified external boundary condition) moving in the given direction.
The precise order of sweep is such that as the solution for one cell is
obtained, the cell provides sufficient boundary conditions for the
solution of an adjacent cell. Hence, cells sharing a given side share
the value of the angular flux on that side. Knowledge of the flux on all
incoming sides of a cell is sufficient to solve for all outgoing sides.
Once the angular flux has been determined for all sides of the cell for
the given direction, it is possible to use a neutron balance to compute
the average value of the angular flux within the cell.}(hj
h j
hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh j
hhubhM)}(hXThe sweeping of cells continues for a given direction until all cell
fluxes have been calculated. The procedure is then repeated for the next
direction until all directions have been computed. At this point, the
cell average angular fluxes are known for each cell for each direction
used. Numerical quadrature can then be used to determine the average
scalar flux in each cell in the problem domain. The scalar fluxes are
used to determine fission and scattering reaction rates in each cell and
to update the value of the cell average source, Q. The process is
repeated, and the iteration continues until all scalar fluxes converge
to within a specified tolerance.h]h/XThe sweeping of cells continues for a given direction until all cell
fluxes have been calculated. The procedure is then repeated for the next
direction until all directions have been computed. At this point, the
cell average angular fluxes are known for each cell for each direction
used. Numerical quadrature can then be used to determine the average
scalar flux in each cell in the problem domain. The scalar fluxes are
used to determine fission and scattering reaction rates in each cell and
to update the value of the cell average source, Q. The process is
repeated, and the iteration continues until all scalar fluxes converge
to within a specified tolerance.}(hj
h j
hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh j
hhubhM)}(hXbThis approach can be performed assuming a single energy group or any
number of discretized energy groups. The multigroup approach used in the
ESC method is the standard approach used in most multigroup methods and
is independent of the shape of each computational cell. Hence, the
details of the multigroup formalism will be omitted from this
discussion.h]h/XbThis approach can be performed assuming a single energy group or any
number of discretized energy groups. The multigroup approach used in the
ESC method is the standard approach used in most multigroup methods and
is independent of the shape of each computational cell. Hence, the
details of the multigroup formalism will be omitted from this
discussion.}(hj
h jhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh j
hhubh)}(h.. _9-2-2-3-3:h]h}(h]h]h]h]h]hid27uhh
hMh j
hhh!h"ubeh}(h](relationships-between-cellsj
eh]h](relationships between cells 9-2-2-3-2eh]h]uhh#h j_hhh!h"hMj}j*j
sj}j
j
subh$)}(hhh](h))}(h$The set of characteristic directionsh]h/$The set of characteristic directions}(hj4h j2hhh!NhNubah}(h]h]h]h]h]uhh(h j/hhh!h"hMubhM)}(hXThe characteristic solution to the transport equation gives only the
angular flux in the direction of the characteristic direction vector |Omk|.
To compute interaction rates within a cell, one must compute scalar
fluxes. In computing the scalar flux from the set of angular fluxes, it
is convenient to choose the set of characteristic directions from an
appropriate quadrature set. Then the set of computed angular fluxes can
be combined with appropriate directional weights and summed to obtain a
scalar flux solution within a cell. Therefore, it is most appropriate to
choose characteristic directions from an established set of base points
and weights. Such quadrature sets that have been developed and used in
numerous earlier discrete- ordinates approaches are used in NEWT. No
restriction is placed on the nature or order of the quadrature set, as
long as it is sufficient to adequately represent the scalar flux from
computed angular fluxes.h](h/The characteristic solution to the transport equation gives only the
angular flux in the direction of the characteristic direction vector }(hThe characteristic solution to the transport equation gives only the
angular flux in the direction of the characteristic direction vector h j@hhh!NhNubjY)}(h:math:`\Omega_{k}`h]h/
\Omega_{k}}(hhh jIhhh!NhNubah}(h]h]h]h]h]uhjXh!NhNh j@hhubh/X%.
To compute interaction rates within a cell, one must compute scalar
fluxes. In computing the scalar flux from the set of angular fluxes, it
is convenient to choose the set of characteristic directions from an
appropriate quadrature set. Then the set of computed angular fluxes can
be combined with appropriate directional weights and summed to obtain a
scalar flux solution within a cell. Therefore, it is most appropriate to
choose characteristic directions from an established set of base points
and weights. Such quadrature sets that have been developed and used in
numerous earlier discrete- ordinates approaches are used in NEWT. No
restriction is placed on the nature or order of the quadrature set, as
long as it is sufficient to adequately represent the scalar flux from
computed angular fluxes.}(hX%.
To compute interaction rates within a cell, one must compute scalar
fluxes. In computing the scalar flux from the set of angular fluxes, it
is convenient to choose the set of characteristic directions from an
appropriate quadrature set. Then the set of computed angular fluxes can
be combined with appropriate directional weights and summed to obtain a
scalar flux solution within a cell. Therefore, it is most appropriate to
choose characteristic directions from an established set of base points
and weights. Such quadrature sets that have been developed and used in
numerous earlier discrete- ordinates approaches are used in NEWT. No
restriction is placed on the nature or order of the quadrature set, as
long as it is sufficient to adequately represent the scalar flux from
computed angular fluxes.h j@hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j/hhubh)}(h.. _9-2-2-3-4:h]h}(h]h]h]h]h]hid28uhh
hMh j/hhh!h"ubeh}(h]($the-set-of-characteristic-directionsj#eh]h]($the set of characteristic directions 9-2-2-3-3eh]h]uhh#h j_hhh!h"hMj}jsjsj}j#jsubh$)}(hhh](h))}(hAngular flux at a cell boundaryh]h/Angular flux at a cell boundary}(hj}h j{hhh!NhNubah}(h]h]h]h]h]uhh(h jxhhh!h"hMubhM)}(hXAs in the development of the SC method, as well as most
finite-difference methods, the ESC approach does not explicitly
determine the flux distribution as a function of position along the
sides of a computational cell. Instead, the angular flux on each cell
side is represented in terms of the average angular flux along the
length of the side. This is sufficient to determine the net leakage
across each cell side, which is needed in order to maintain a cell
balance. An average value of the flux for an incoming side must be
specified from a boundary condition or from the prior solution of an
adjacent cell. The average flux along a given outgoing side can be
computed by integrating the flux along the side and dividing by the
length of the side. However, the form of the distribution of the angular
flux on the side must be known to perform this integration. This
distribution can be determined from the properties of the cell and from
the average flux on each of the known incoming sides.h]h/XAs in the development of the SC method, as well as most
finite-difference methods, the ESC approach does not explicitly
determine the flux distribution as a function of position along the
sides of a computational cell. Instead, the angular flux on each cell
side is represented in terms of the average angular flux along the
length of the side. This is sufficient to determine the net leakage
across each cell side, which is needed in order to maintain a cell
balance. An average value of the flux for an incoming side must be
specified from a boundary condition or from the prior solution of an
adjacent cell. The average flux along a given outgoing side can be
computed by integrating the flux along the side and dividing by the
length of the side. However, the form of the distribution of the angular
flux on the side must be known to perform this integration. This
distribution can be determined from the properties of the cell and from
the average flux on each of the known incoming sides.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jxhhubhM)}(hX>Because the characteristic solution [Eq. :eq:`eq9-2-6`] allows calculation of
the angular flux at any point *s* in a single cell given an initial
condition, the exact value of the flux can be computed at any point on
any outgoing side if the flux along each incoming side is known. As an
initial condition, it is assumed that the angular flux in some
characteristic direction is known at some starting point, *s* = 0
[i.e., ψ(0) = ψ\ :sub:`0`], on an incoming side. To determine the flux at
some point on an outgoing side, one need know only the distance *s*
measured along a characteristic direction to the appropriate incoming
side. This method can then be expanded to determine a functional form of
the flux for every point on the outgoing side, which can be integrated
to produce the average outgoing flux on the side.h](h/*Because the characteristic solution [Eq. }(h*Because the characteristic solution [Eq. h jhhh!NhNubj)}(h
:eq:`eq9-2-6`h]jM)}(hjh]h/eq9-2-6}(hhh jubah}(h]h](jEeqeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjXreftypejrefexplicitrefwarnjWeq9-2-6uhjh!h"hM#h jubh/6] allows calculation of
the angular flux at any point }(h6] allows calculation of
the angular flux at any point h jhhh!NhNubj)}(h*s*h]h/s}(hhh jubah}(h]h]h]h]h]uhjh jubh/X* in a single cell given an initial
condition, the exact value of the flux can be computed at any point on
any outgoing side if the flux along each incoming side is known. As an
initial condition, it is assumed that the angular flux in some
characteristic direction is known at some starting point, }(hX* in a single cell given an initial
condition, the exact value of the flux can be computed at any point on
any outgoing side if the flux along each incoming side is known. As an
initial condition, it is assumed that the angular flux in some
characteristic direction is known at some starting point, h jhhh!NhNubj)}(h*s*h]h/s}(hhh jubah}(h]h]h]h]h]uhjh jubh/ = 0
[i.e., ψ(0) = ψ }(h = 0
[i.e., ψ(0) = ψ\ h jhhh!NhNubj)}(h:sub:`0`h]h/0}(hhh jubah}(h]h]h]h]h]uhjh jubh/q], on an incoming side. To determine the flux at
some point on an outgoing side, one need know only the distance }(hq], on an incoming side. To determine the flux at
some point on an outgoing side, one need know only the distance h jhhh!NhNubj)}(h*s*h]h/s}(hhh jubah}(h]h]h]h]h]uhjh jubh/X
measured along a characteristic direction to the appropriate incoming
side. This method can then be expanded to determine a functional form of
the flux for every point on the outgoing side, which can be integrated
to produce the average outgoing flux on the side.}(hX
measured along a characteristic direction to the appropriate incoming
side. This method can then be expanded to determine a functional form of
the flux for every point on the outgoing side, which can be integrated
to produce the average outgoing flux on the side.h jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM#h jxhhubhM)}(hXkTo develop a mathematical relationship between two arbitrary sides of a
cell, one should first consider two arbitrary coplanar line segments in
space whose endpoints each lie on a pair of parallel lines laid in the
direction |Omk|, as shown in :numref:`fig9-2-3`. Points B\ :sub:`1` and B\ :sub:`2`
can be considered to be the “projections” of A\ :sub:`1` and
A\ :sub:`2`, respectively, relative to |Omk|. Because *s* is the distance
between a point on segment A and its projection on segment B, it can be
seen that *s* varies linearly in moving from the “beginning” to the
“end” of the pair of segments.h](h/To develop a mathematical relationship between two arbitrary sides of a
cell, one should first consider two arbitrary coplanar line segments in
space whose endpoints each lie on a pair of parallel lines laid in the
direction }(hTo develop a mathematical relationship between two arbitrary sides of a
cell, one should first consider two arbitrary coplanar line segments in
space whose endpoints each lie on a pair of parallel lines laid in the
direction h jhhh!NhNubjY)}(hjKh]h/
\Omega_{k}}(hhh jhhh!NhNubah}(h]h]h]h]h]uhjXh!NhNh jhhubh/, as shown in }(h, as shown in h jhhh!NhNubj)}(h:numref:`fig9-2-3`h]jM)}(hj2h]h/fig9-2-3}(hhh j4ubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh j0ubah}(h]h]h]h]h]refdochj refdomainj>reftypenumrefrefexplicitrefwarnjWfig9-2-3uhjh!h"hM0h jubh/
. Points B }(h
. Points B\ h jhhh!NhNubj)}(h:sub:`1`h]h/1}(hhh jUubah}(h]h]h]h]h]uhjh jubh/ and B }(h and B\ h jhhh!NhNubj)}(h:sub:`2`h]h/2}(hhh jhubah}(h]h]h]h]h]uhjh jubh/5
can be considered to be the “projections” of A }(h5
can be considered to be the “projections” of A\ h jhhh!NhNubj)}(h:sub:`1`h]h/1}(hhh j{ubah}(h]h]h]h]h]uhjh jubh/ and
A }(h and
A\ h jhhh!NhNubj)}(h:sub:`2`h]h/2}(hhh jubah}(h]h]h]h]h]uhjh jubh/, respectively, relative to }(h, respectively, relative to h jhhh!NhNubjY)}(hjKh]h/
\Omega_{k}}(hhh jhhh!NhNubah}(h]h]h]h]h]uhjXh!NhNh jhhubh/
. Because }(h
. Because h jhhh!NhNubj)}(h*s*h]h/s}(hhh jubah}(h]h]h]h]h]uhjh jubh/e is the distance
between a point on segment A and its projection on segment B, it can be
seen that }(he is the distance
between a point on segment A and its projection on segment B, it can be
seen that h jhhh!NhNubj)}(h*s*h]h/s}(hhh jubah}(h]h]h]h]h]uhjh jubh/] varies linearly in moving from the “beginning” to the
“end” of the pair of segments.}(h] varies linearly in moving from the “beginning” to the
“end” of the pair of segments.h jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM0h jxhhubh)}(h
.. _fig9-2-3:h]h}(h]h]h]h]h]hfig9-2-3uhh
hM:h jxhhh!h"ubj)}(hhh](j)}(hs.. figure:: figs/NEWT/fig3.png
:align: center
:width: 400
Line endpoints for computation of average fluxes.
h]h}(h]h]h]h]h]width400urifigs/NEWT/fig3.pngj*}j,jsuhjh jh!h"hM?ubj.)}(h1Line endpoints for computation of average fluxes.h]h/1Line endpoints for computation of average fluxes.}(hjh jubah}(h]h]h]h]h]uhj-h!h"hM?h jubeh}(h](id161jeh]h]fig9-2-3ah]h]jEcenteruhjhM?h jxhhh!h"j}jjsj}jjsubhM)}(hIf α is the distance along segment B measured from endpoint B\ :sub:`1`
and B has a total length L, then the distance *s* between A and B along
direction |Omk| can be written as a linear function in terms of the
position α:h](h/BIf α is the distance along segment B measured from endpoint B }(hBIf α is the distance along segment B measured from endpoint B\ h jhhh!NhNubj)}(h:sub:`1`h]h/1}(hhh jubah}(h]h]h]h]h]uhjh jubh/0
and B has a total length L, then the distance }(h0
and B has a total length L, then the distance h jhhh!NhNubj)}(h*s*h]h/s}(hhh j1ubah}(h]h]h]h]h]uhjh jubh/! between A and B along
direction }(h! between A and B along
direction h jhhh!NhNubjY)}(hjKh]h/
\Omega_{k}}(hhh jDhhh!NhNubah}(h]h]h]h]h]uhjXh!NhNh jhhubh/B can be written as a linear function in terms of the
position α:}(hB can be written as a linear function in terms of the
position α:h jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMAh jxhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-13uhh
h jxhhh!h"hNubj))}(h;s(\alpha)=s_{1}+\left(\frac{s_{2}-s_{1}}{L}\right) \alpha ,h]h/;s(\alpha)=s_{1}+\left(\frac{s_{2}-s_{1}}{L}\right) \alpha ,}(hhh jfubah}(h]jeah]h]h]h]docnamehjnumberK
labeleq9-2-13nowrapj=j>uhj(h!h"hMFh jxhhj}j}jej\subhM)}(hXwhere *s*\ :sub:`1` and *s*\ :sub:`2` are related to the distances along
the characteristic direction between A\ :sub:`1`, B\ :sub:`1` and
A\ :sub:`2`, B\ :sub:`2`, respectively. (It is important to note that
the length *s* is the same as the distance between the endpoints only
when the characteristic vector lies in the plane of the computational
cell. This is not necessarily the case, depending on the choice of
quadrature directions. This situation is discussed in more detail
later.)h](h/where }(hwhere h j{hhh!NhNubj)}(h*s*h]h/s}(hhh jubah}(h]h]h]h]h]uhjh j{ubh/ }(h\ h j{hhh!NhNubj)}(h:sub:`1`h]h/1}(hhh jubah}(h]h]h]h]h]uhjh j{ubh/ and }(h and h j{hhh!NhNubj)}(h*s*h]h/s}(hhh jubah}(h]h]h]h]h]uhjh j{ubh/ }(hjh j{ubj)}(h:sub:`2`h]h/2}(hhh jubah}(h]h]h]h]h]uhjh j{ubh/L are related to the distances along
the characteristic direction between A }(hL are related to the distances along
the characteristic direction between A\ h j{hhh!NhNubj)}(h:sub:`1`h]h/1}(hhh jubah}(h]h]h]h]h]uhjh j{ubh/, B }(h, B\ h j{hhh!NhNubj)}(h:sub:`1`h]h/1}(hhh jubah}(h]h]h]h]h]uhjh j{ubh/ and
A }(h and
A\ h j{hhh!NhNubj)}(h:sub:`2`h]h/2}(hhh jubah}(h]h]h]h]h]uhjh j{ubh/, B }(hjh j{ubj)}(h:sub:`2`h]h/2}(hhh jubah}(h]h]h]h]h]uhjh j{ubh/9, respectively. (It is important to note that
the length }(h9, respectively. (It is important to note that
the length h j{hhh!NhNubj)}(h*s*h]h/s}(hhh jubah}(h]h]h]h]h]uhjh j{ubh/X
is the same as the distance between the endpoints only
when the characteristic vector lies in the plane of the computational
cell. This is not necessarily the case, depending on the choice of
quadrature directions. This situation is discussed in more detail
later.)}(hX
is the same as the distance between the endpoints only
when the characteristic vector lies in the plane of the computational
cell. This is not necessarily the case, depending on the choice of
quadrature directions. This situation is discussed in more detail
later.)h j{hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMKh jxhhubhM)}(hIf ψ(α) is the angular flux on side B at a distance α from B\ :sub:`1`,
then :math:`\bar{\psi}_{\mathrm{B}}`, the average value of ψ on B, is given byh](h/CIf ψ(α) is the angular flux on side B at a distance α from B }(hCIf ψ(α) is the angular flux on side B at a distance α from B\ h j3hhh!NhNubj)}(h:sub:`1`h]h/1}(hhh j<ubah}(h]h]h]h]h]uhjh j3ubh/,
then }(h,
then h j3hhh!NhNubjY)}(h:math:`\bar{\psi}_{\mathrm{B}}`h]h/\bar{\psi}_{\mathrm{B}}}(hhh jOubah}(h]h]h]h]h]uhjXh j3ubh/+, the average value of ψ on B, is given by}(h+, the average value of ψ on B, is given byh j3hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMTh jxhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-14uhh
h jxhhh!h"hNubj))}(hT\bar{\psi}_{B}=\frac{\int_{0}^{L} \psi(s(\alpha)) d \alpha}{\int_{0}^{L} d \alpha} .h]h/T\bar{\psi}_{B}=\frac{\int_{0}^{L} \psi(s(\alpha)) d \alpha}{\int_{0}^{L} d \alpha} .}(hhh jrubah}(h]jqah]h]h]h]docnamehjnumberKlabeleq9-2-14nowrapj=j>uhj(h!h"hMWh jxhhj}j}jqjhsubhM)}(hEquation :eq:`eq9-2-6`, the solution to the characteristic equation in the
step approximation, can be rewritten in terms of the average known
angular flux on side Ah](h/
Equation }(h
Equation h jhhh!NhNubj)}(h
:eq:`eq9-2-6`h]jM)}(hjh]h/eq9-2-6}(hhh jubah}(h]h](jEeqeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjXreftypejrefexplicitrefwarnjWeq9-2-6uhjh!h"hM\h jubh/, the solution to the characteristic equation in the
step approximation, can be rewritten in terms of the average known
angular flux on side A}(h, the solution to the characteristic equation in the
step approximation, can be rewritten in terms of the average known
angular flux on side Ah jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM\h jxhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-15uhh
h jxhhh!h"hNubj))}(hY\psi_{B}(s)=\left(\bar{\psi}_{A}-Q / \sigma_{t}\right) e^{-\sigma_{t} s}+Q / \sigma_{t} .h]h/Y\psi_{B}(s)=\left(\bar{\psi}_{A}-Q / \sigma_{t}\right) e^{-\sigma_{t} s}+Q / \sigma_{t} .}(hhh jubah}(h]jah]h]h]h]docnamehjnumberKlabeleq9-2-15nowrapj=j>uhj(h!h"hM`h jxhhj}j}jjsubhM)}(haInserting Eqs. :eq:`eq9-2-13` and :eq:`eq9-2-15` into Eq. :eq:`eq9-2-14` and simplifying
yieldsh](h/Inserting Eqs. }(hInserting Eqs. h jhhh!NhNubj)}(h:eq:`eq9-2-13`h]jM)}(hjh]h/eq9-2-13}(hhh jubah}(h]h](jEeqeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjXreftypejrefexplicitrefwarnjWeq9-2-13uhjh!h"hMeh jubh/ and }(h and h jhhh!NhNubj)}(h:eq:`eq9-2-15`h]jM)}(hjh]h/eq9-2-15}(hhh jubah}(h]h](jEeqeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjXreftypejrefexplicitrefwarnjWeq9-2-15uhjh!h"hMeh jubh/ into Eq. }(h into Eq. h jhhh!NhNubj)}(h:eq:`eq9-2-14`h]jM)}(hj)h]h/eq9-2-14}(hhh j+ubah}(h]h](jEeqeh]h]h]uhjLh j'ubah}(h]h]h]h]h]refdochj refdomainjXreftypej5refexplicitrefwarnjWeq9-2-14uhjh!h"hMeh jubh/ and simplifying
yields}(h and simplifying
yieldsh jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMeh jxhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-16uhh
h jxhhh!h"hNubj))}(h\bar{\psi}_{B}=\frac{1}{L} \int_{0}^{L}\left[\left(\bar{\psi}_{A}-Q / \sigma_{t}\right) \exp \left(-\sigma_{t}\left(s_{1}+\left(\frac{s_{2}-s_{1}}{L}\right) \alpha\right)\right)+Q / \sigma_{t}\right] d \alpha .h]h/\bar{\psi}_{B}=\frac{1}{L} \int_{0}^{L}\left[\left(\bar{\psi}_{A}-Q / \sigma_{t}\right) \exp \left(-\sigma_{t}\left(s_{1}+\left(\frac{s_{2}-s_{1}}{L}\right) \alpha\right)\right)+Q / \sigma_{t}\right] d \alpha .}(hhh jZubah}(h]jYah]h]h]h]docnamehjnumberKlabeleq9-2-16nowrapj=j>uhj(h!h"hMhh jxhhj}j}jYjPsubhM)}(hFor the special case in which A and B are parallel,
*s*\ :sub:`1` = *s*\ :sub:`2` and the second term in the exponential
drops out. Equation :eq:`eq9-2-16` can easily be integrated to obtainh](h/4For the special case in which A and B are parallel,
}(h4For the special case in which A and B are parallel,
h johhh!NhNubj)}(h*s*h]h/s}(hhh jxubah}(h]h]h]h]h]uhjh joubh/ }(h\ h johhh!NhNubj)}(h:sub:`1`h]h/1}(hhh jubah}(h]h]h]h]h]uhjh joubh/ = }(h = h johhh!NhNubj)}(h*s*h]h/s}(hhh jubah}(h]h]h]h]h]uhjh joubh/ }(hjh joubj)}(h:sub:`2`h]h/2}(hhh jubah}(h]h]h]h]h]uhjh joubh/= and the second term in the exponential
drops out. Equation }(h= and the second term in the exponential
drops out. Equation h johhh!NhNubj)}(h:eq:`eq9-2-16`h]jM)}(hjh]h/eq9-2-16}(hhh jubah}(h]h](jEeqeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjXreftypejrefexplicitrefwarnjWeq9-2-16uhjh!h"hMmh joubh/# can easily be integrated to obtain}(h# can easily be integrated to obtainh johhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMmh jxhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-17uhh
h jxhhh!h"hNubj))}(h`\bar{\psi}_{B}=\left(\bar{\psi}_{A}-Q / \sigma_{t}\right) e^{-\sigma_{t} s_{1}}+Q / \sigma_{t} .h]h/`\bar{\psi}_{B}=\left(\bar{\psi}_{A}-Q / \sigma_{t}\right) e^{-\sigma_{t} s_{1}}+Q / \sigma_{t} .}(hhh jubah}(h]jah]h]h]h]docnamehjnumberKlabeleq9-2-17nowrapj=j>uhj(h!h"hMqh jxhhj}j}jjsubhM)}(heIn the more general case, *s*\ :sub:`1` ≠ *s*\ :sub:`2`, the result is
slightly more complicated:h](h/In the more general case, }(hIn the more general case, h jhhh!NhNubj)}(h*s*h]h/s}(hhh jubah}(h]h]h]h]h]uhjh jubh/ }(h\ h jhhh!NhNubj)}(h:sub:`1`h]h/1}(hhh j'ubah}(h]h]h]h]h]uhjh jubh/ ≠ }(h ≠ h jhhh!NhNubj)}(h*s*h]h/s}(hhh j:ubah}(h]h]h]h]h]uhjh jubh/ }(hj&h jubj)}(h:sub:`2`h]h/2}(hhh jLubah}(h]h]h]h]h]uhjh jubh/*, the result is
slightly more complicated:}(h*, the result is
slightly more complicated:h jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMvh jxhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-18uhh
h jxhhh!h"hNubj))}(h\bar{\psi}_{B}=\frac{\left(\bar{\psi}_{A}-Q / \sigma_{t}\right)}{\sigma_{t}\left(s_{2}-s_{1}\right)}\left[e^{-\sigma_{t} s_{1}}-e^{-\sigma_{t} s_{2}}\right]+Q / \sigma_{t} .h]h/\bar{\psi}_{B}=\frac{\left(\bar{\psi}_{A}-Q / \sigma_{t}\right)}{\sigma_{t}\left(s_{2}-s_{1}\right)}\left[e^{-\sigma_{t} s_{1}}-e^{-\sigma_{t} s_{2}}\right]+Q / \sigma_{t} .}(hhh joubah}(h]jnah]h]h]h]docnamehjnumberKlabeleq9-2-18nowrapj=j>uhj(h!h"hMyh jxhhj}j}jnjesubhM)}(hUEquations :eq:`eq9-2-17` and :eq:`eq9-2-18` can also be written in a simplified form:h](h/
Equations }(h
Equations h jhhh!NhNubj)}(h:eq:`eq9-2-17`h]jM)}(hjh]h/eq9-2-17}(hhh jubah}(h]h](jEeqeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjXreftypejrefexplicitrefwarnjWeq9-2-17uhjh!h"hM~h jubh/ and }(h and h jhhh!NhNubj)}(h:eq:`eq9-2-18`h]jM)}(hjh]h/eq9-2-18}(hhh jubah}(h]h](jEeqeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjXreftypejrefexplicitrefwarnjWeq9-2-18uhjh!h"hM~h jubh/* can also be written in a simplified form:}(h* can also be written in a simplified form:h jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM~h jxhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-19uhh
h jxhhh!h"hNubj))}(hS\bar{\psi}_{B}=\beta_{A B} \bar{\psi}_{A}+\left(1-\beta_{A B}\right) Q / \sigma_{t}h]h/S\bar{\psi}_{B}=\beta_{A B} \bar{\psi}_{A}+\left(1-\beta_{A B}\right) Q / \sigma_{t}}(hhh jubah}(h]jah]h]h]h]docnamehjnumberKlabeleq9-2-19nowrapj=j>uhj(h!h"hMh jxhhj}j}jjsubhM)}(hwhereh]h/where}(hjh jhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jxhhubjP)}(hhh]j))}(h\beta_{A B}=\left\{\begin{array}{cc}
\frac{e^{-\sigma_{t} s_{1}}-e^{-\sigma_{t} s_{2}}}{\sigma_{t}\left(s_{2}-s_{1}\right)} & s_{1} \neq s_{2} \\
e^{-\sigma_{t} s_{1}} & s_{1}=s_{2}
\end{array}\right.h]h/\beta_{A B}=\left\{\begin{array}{cc}
\frac{e^{-\sigma_{t} s_{1}}-e^{-\sigma_{t} s_{2}}}{\sigma_{t}\left(s_{2}-s_{1}\right)} & s_{1} \neq s_{2} \\
e^{-\sigma_{t} s_{1}} & s_{1}=s_{2}
\end{array}\right.}(hhh j ubah}(h]h]h]h]h]docnamehjnumberNlabelNnowrapj=j>uhj(h!h"hMh jubah}(h]h]h]h]h]uhjOh jxhhh!NhNubhM)}(hXaThus far, this development has considered only the special case where
contributions to side B are the result only of the cell internal source
and a single incoming side (i.e., side A). For an arbitrarily shaped
cell and discrete direction |Omk|, it is likely that the outgoing side would
receive contributions from two or more incoming sides, as illustrated in
:numref:`fig9-2-4`, for a cell with three incoming sides (X, Y, and Z)
contributing to the flux on a single outgoing side (B). In such a
situation, the outgoing side can be subdivided into multiple components.
Side B of :numref:`fig9-2-4` can be represented by three components,
B\ :sub:`X`, B\ :sub:`Y`, and B\ :sub:`Z`, representing contributions
from line segments X, Y, and Z, respectively. The average angular flux
:math:`\bar{\psi}` can be computed for each component of side B using
Eq. :eq:`eq9-2-19`; then :math:`\bar{\psi}_{B}`, the average flux for the entire length of
B, can be calculated by the length-weighted average of each component.
In general, for a given side B composed of *n* components, the average
flux of the side is given byh](h/Thus far, this development has considered only the special case where
contributions to side B are the result only of the cell internal source
and a single incoming side (i.e., side A). For an arbitrarily shaped
cell and discrete direction }(hThus far, this development has considered only the special case where
contributions to side B are the result only of the cell internal source
and a single incoming side (i.e., side A). For an arbitrarily shaped
cell and discrete direction h j!hhh!NhNubjY)}(hjKh]h/
\Omega_{k}}(hhh j*hhh!NhNubah}(h]h]h]h]h]uhjXh!NhNh j!hhubh/u, it is likely that the outgoing side would
receive contributions from two or more incoming sides, as illustrated in
}(hu, it is likely that the outgoing side would
receive contributions from two or more incoming sides, as illustrated in
h j!hhh!NhNubj)}(h:numref:`fig9-2-4`h]jM)}(hj>h]h/fig9-2-4}(hhh j@ubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh j<ubah}(h]h]h]h]h]refdochj refdomainjJreftypenumrefrefexplicitrefwarnjWfig9-2-4uhjh!h"hMh j!ubh/, for a cell with three incoming sides (X, Y, and Z)
contributing to the flux on a single outgoing side (B). In such a
situation, the outgoing side can be subdivided into multiple components.
Side B of }(h, for a cell with three incoming sides (X, Y, and Z)
contributing to the flux on a single outgoing side (B). In such a
situation, the outgoing side can be subdivided into multiple components.
Side B of h j!hhh!NhNubj)}(h:numref:`fig9-2-4`h]jM)}(hjch]h/fig9-2-4}(hhh jeubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jaubah}(h]h]h]h]h]refdochj refdomainjoreftypenumrefrefexplicitrefwarnjWfig9-2-4uhjh!h"hMh j!ubh/, can be represented by three components,
B }(h, can be represented by three components,
B\ h j!hhh!NhNubj)}(h:sub:`X`h]h/X}(hhh jubah}(h]h]h]h]h]uhjh j!ubh/, B }(h, B\ h j!hhh!NhNubj)}(h:sub:`Y`h]h/Y}(hhh jubah}(h]h]h]h]h]uhjh j!ubh/ , and B }(h , and B\ h j!hhh!NhNubj)}(h:sub:`Z`h]h/Z}(hhh jubah}(h]h]h]h]h]uhjh j!ubh/d, representing contributions
from line segments X, Y, and Z, respectively. The average angular flux
}(hd, representing contributions
from line segments X, Y, and Z, respectively. The average angular flux
h j!hhh!NhNubjY)}(h:math:`\bar{\psi}`h]h/
\bar{\psi}}(hhh jubah}(h]h]h]h]h]uhjXh j!ubh/: can be computed for each component of side B using
Eq. }(h: can be computed for each component of side B using
Eq. h j!hhh!NhNubj)}(h:eq:`eq9-2-19`h]jM)}(hjh]h/eq9-2-19}(hhh jubah}(h]h](jEeqeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjXreftypejrefexplicitrefwarnjWeq9-2-19uhjh!h"hMh j!ubh/; then }(h; then h j!hhh!NhNubjY)}(h:math:`\bar{\psi}_{B}`h]h/\bar{\psi}_{B}}(hhh jubah}(h]h]h]h]h]uhjXh j!ubh/, the average flux for the entire length of
B, can be calculated by the length-weighted average of each component.
In general, for a given side B composed of }(h, the average flux for the entire length of
B, can be calculated by the length-weighted average of each component.
In general, for a given side B composed of h j!hhh!NhNubj)}(h*n*h]h/n}(hhh jubah}(h]h]h]h]h]uhjh j!ubh/5 components, the average
flux of the side is given by}(h5 components, the average
flux of the side is given byh j!hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jxhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-20uhh
h jxhhh!h"hNubj))}(h<\bar{\psi}_{B}=\sum_{i=1}^{n} \frac{\bar{\psi}_{i} i}{L_{B}}h]h/<\bar{\psi}_{B}=\sum_{i=1}^{n} \frac{\bar{\psi}_{i} i}{L_{B}}}(hhh j+ubah}(h]j*ah]h]h]h]docnamehjnumberKlabeleq9-2-20nowrapj=j>uhj(h!h"hMh jxhhj}j}j*j!subhM)}(hwhereh]h/where}(hjBh j@hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jxhhubjP)}(hhh](hM)}(hL:math:`\ell_{i}` is the length of the projection of the ith side onto B, andh](jY)}(h:math:`\ell_{i}`h]h/\ell_{i}}(hhh jUubah}(h]h]h]h]h]uhjXh jQubh/< is the length of the projection of the ith side onto B, and}(h< is the length of the projection of the ith side onto B, andh jQubeh}(h]h]h]h]h]uhhLh!h"hMh jNubhM)}(hh:math:`\bar{\psi}_{i}` is the average flux computed for segment B\ :sub:`i` due to the
flux on side *i*h](jY)}(h:math:`\bar{\psi}_{i}`h]h/\bar{\psi}_{i}}(hhh jrubah}(h]h]h]h]h]uhjXh jnubh/. is the average flux computed for segment B }(h. is the average flux computed for segment B\ h jnubj)}(h:sub:`i`h]h/i}(hhh jubah}(h]h]h]h]h]uhjh jnubh/ due to the
flux on side }(h due to the
flux on side h jnubj)}(h*i*h]h/i}(hhh jubah}(h]h]h]h]h]uhjh jnubeh}(h]h]h]h]h]uhhLh!h"hMh jNubeh}(h]h]h]h]h]uhjOh jxhhh!h"hNubhM)}(hXUsing Eqs. :eq:`eq9-2-19` and :eq:`eq9-2-20`, one can compute the average flux on
each of the outgoing sides for a given cell, once the angular flux on
each incoming side is known. At this point, only distances *s*\ :sub:`1`
and *s*\ :sub:`2` and the lengths :math:`\ell_{i}` and L need be determined to estimate
fluxes in an iterative process. These can be computed from the geometry
of the cell and the direction |Omk|.h](h/Using Eqs. }(hUsing Eqs. h jhhh!NhNubj)}(h:eq:`eq9-2-19`h]jM)}(hjh]h/eq9-2-19}(hhh jubah}(h]h](jEeqeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjXreftypejrefexplicitrefwarnjWeq9-2-19uhjh!h"hMh jubh/ and }(h and h jhhh!NhNubj)}(h:eq:`eq9-2-20`h]jM)}(hjh]h/eq9-2-20}(hhh jubah}(h]h](jEeqeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjXreftypejrefexplicitrefwarnjWeq9-2-20uhjh!h"hMh jubh/, one can compute the average flux on
each of the outgoing sides for a given cell, once the angular flux on
each incoming side is known. At this point, only distances }(h, one can compute the average flux on
each of the outgoing sides for a given cell, once the angular flux on
each incoming side is known. At this point, only distances h jhhh!NhNubj)}(h*s*h]h/s}(hhh jubah}(h]h]h]h]h]uhjh jubh/ }(h\ h jhhh!NhNubj)}(h:sub:`1`h]h/1}(hhh jubah}(h]h]h]h]h]uhjh jubh/
and }(h
and h jhhh!NhNubj)}(h*s*h]h/s}(hhh j'ubah}(h]h]h]h]h]uhjh jubh/ }(hjh jubj)}(h:sub:`2`h]h/2}(hhh j9ubah}(h]h]h]h]h]uhjh jubh/ and the lengths }(h and the lengths h jhhh!NhNubjY)}(h:math:`\ell_{i}`h]h/\ell_{i}}(hhh jLubah}(h]h]h]h]h]uhjXh jubh/ and L need be determined to estimate
fluxes in an iterative process. These can be computed from the geometry
of the cell and the direction }(h and L need be determined to estimate
fluxes in an iterative process. These can be computed from the geometry
of the cell and the direction h jhhh!NhNubjY)}(hjKh]h/
\Omega_{k}}(hhh j_hhh!NhNubah}(h]h]h]h]h]uhjXh!NhNh jhhubh/.}(hhh jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jxhhubh)}(h
.. _fig9-2-4:h]h}(h]h]h]h]h]hfig9-2-4uhh
hMh jxhhh!h"ubj)}(hhh](j)}(h.. figure:: figs/NEWT/fig4.png
:align: center
:width: 500
Contributions of multiple incoming sides to an outgoing side.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig4.pngj*}j,jsuhjh jh!h"hMubj.)}(h=Contributions of multiple incoming sides to an outgoing side.h]h/=Contributions of multiple incoming sides to an outgoing side.}(hjh jubah}(h]h]h]h]h]uhj-h!h"hMh jubeh}(h](id162jeh]h]fig9-2-4ah]h]jEcenteruhjhMh jxhhh!h"j}jjvsj}jjvsubh)}(h.. _9-2-2-3-5:h]h}(h]h]h]h]h]hid29uhh
hMh jxhhh!h"ubeh}(h](angular-flux-at-a-cell-boundaryjleh]h](angular flux at a cell boundary 9-2-2-3-4eh]h]uhh#h j_hhh!h"hMj}jjbsj}jljbsubh$)}(hhh](h))}(hGMapping a characteristic vector into the two-dimensional problem domainh]h/GMapping a characteristic vector into the two-dimensional problem domain}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hMubhM)}(hXEven in a 2-D x-y system in which the scalar flux is constant with
respect to the z axis, the angular flux has components in the
z direction. Thus, to obtain the scalar flux at a point on the
x-y plane, one must integrate over the unit sphere in all 4π directions
of |Om|. Recall that the choices of characteristic directions for this model
were selected to be the same as the set of directions composing a
conventional quadrature set. Quadrature sets specified in the
literature :cite:`carlson_transport_1970,carlson_discrete_1965,lee_discrete_1962` and used in other
discrete-ordinates codes :cite:`lathrop_twotran-ii_1973,engle_jr_users_1967` are based on a unit
sphere and are usually specified in terms of μ\ :sub:`k` and η\ :sub:`k`,
the respective x and y components of |Omk|, where is one of a set of discrete
directions composing the quadrature set. Because |Omk| is a unit vector, :math:`\xi_{k}`, the
z component of the direction, is implicit: :math:`\xi_{k}=\sqrt{1-\mu_{k}^{2}-\eta_{k}^{2}}`.
However, because of the 2‑D
nature of the problem, the z component is never explicitly used. It is
therefore sufficient to evaluate the angular flux at a finite number of
points in 4π of |Om| -space in terms of just the μ\ :sub:`k` and η\ :sub:`k`
components of the discrete directions |Omk|. One must recognize, however,
that the length of the path traveled by particles moving in a direction
out of the x-y plane is always longer than the x-y projection of the
path, by a factor of (μ\ :sup:`2` + η\ :sup:`2`)\ :sup:`–1/2`. Thus, for any
path length *s*' measured in the x‑y plane for a given direction |Omk|, the
true path length traveled is *s*, whereh](h/XEven in a 2-D x-y system in which the scalar flux is constant with
respect to the z axis, the angular flux has components in the
z direction. Thus, to obtain the scalar flux at a point on the
x-y plane, one must integrate over the unit sphere in all 4π directions
of }(hXEven in a 2-D x-y system in which the scalar flux is constant with
respect to the z axis, the angular flux has components in the
z direction. Thus, to obtain the scalar flux at a point on the
x-y plane, one must integrate over the unit sphere in all 4π directions
of h jhhh!NhNubjY)}(h:math:`\Omega`h]h/\Omega}(hhh jhhh!NhNubah}(h]h]h]h]h]uhjXh!NhNh jhhubh/. Recall that the choices of characteristic directions for this model
were selected to be the same as the set of directions composing a
conventional quadrature set. Quadrature sets specified in the
literature }(h. Recall that the choices of characteristic directions for this model
were selected to be the same as the set of directions composing a
conventional quadrature set. Quadrature sets specified in the
literature h jhhh!NhNubj)}(hcarlson_transport_1970h]j)}(hjh]h/[carlson_transport_1970]}(hhh jubah}(h]h]h]h]h]uhjh jubah}(h]id30ah]jah]h]h] refdomainjreftypej reftargetjrefwarnsupport_smartquotesuhjh!h"hMh jhhubj)}(hcarlson_discrete_1965h]j)}(hjh]h/[carlson_discrete_1965]}(hhh jubah}(h]h]h]h]h]uhjh jubah}(h]id31ah]jah]h]h] refdomainjreftypej reftargetjrefwarnsupport_smartquotesuhjh!h"hMh jhhubj)}(hlee_discrete_1962h]j)}(hj+h]h/[lee_discrete_1962]}(hhh j-ubah}(h]h]h]h]h]uhjh j)ubah}(h]id32ah]jah]h]h] refdomainjreftypej reftargetj+refwarnsupport_smartquotesuhjh!h"hMh jhhubh/, and used in other
discrete-ordinates codes }(h, and used in other
discrete-ordinates codes h jhhh!NhNubj)}(hlathrop_twotran-ii_1973h]j)}(hjMh]h/[lathrop_twotran-ii_1973]}(hhh jOubah}(h]h]h]h]h]uhjh jKubah}(h]id33ah]jah]h]h] refdomainjreftypej reftargetjMrefwarnsupport_smartquotesuhjh!h"hMh jhhubj)}(hengle_jr_users_1967h]j)}(hjjh]h/[engle_jr_users_1967]}(hhh jlubah}(h]h]h]h]h]uhjh jhubah}(h]id34ah]jah]h]h] refdomainjreftypej reftargetjjrefwarnsupport_smartquotesuhjh!h"hMh jhhubh/F are based on a unit
sphere and are usually specified in terms of μ }(hF are based on a unit
sphere and are usually specified in terms of μ\ h jhhh!NhNubj)}(h:sub:`k`h]h/k}(hhh jubah}(h]h]h]h]h]uhjh jubh/ and η }(h and η\ h jhhh!NhNubj)}(h:sub:`k`h]h/k}(hhh jubah}(h]h]h]h]h]uhjh jubh/(,
the respective x and y components of }(h(,
the respective x and y components of h jhhh!NhNubjY)}(hjKh]h/
\Omega_{k}}(hhh jhhh!NhNubah}(h]h]h]h]h]uhjXh!NhNh jhhubh/U, where is one of a set of discrete
directions composing the quadrature set. Because }(hU, where is one of a set of discrete
directions composing the quadrature set. Because h jhhh!NhNubjY)}(hjKh]h/
\Omega_{k}}(hhh jhhh!NhNubah}(h]h]h]h]h]uhjXh!NhNh jhhubh/ is a unit vector, }(h is a unit vector, h jhhh!NhNubjY)}(h:math:`\xi_{k}`h]h/\xi_{k}}(hhh jubah}(h]h]h]h]h]uhjXh jubh/2, the
z component of the direction, is implicit: }(h2, the
z component of the direction, is implicit: h jhhh!NhNubjY)}(h1:math:`\xi_{k}=\sqrt{1-\mu_{k}^{2}-\eta_{k}^{2}}`h]h/)\xi_{k}=\sqrt{1-\mu_{k}^{2}-\eta_{k}^{2}}}(hhh jubah}(h]h]h]h]h]uhjXh jubh/.
However, because of the 2‑D
nature of the problem, the z component is never explicitly used. It is
therefore sufficient to evaluate the angular flux at a finite number of
points in 4π of }(h.
However, because of the 2‑D
nature of the problem, the z component is never explicitly used. It is
therefore sufficient to evaluate the angular flux at a finite number of
points in 4π of h jhhh!NhNubjY)}(hjh]h/\Omega}(hhh jhhh!NhNubah}(h]h]h]h]h]uhjXh!NhNh jhhubh/! -space in terms of just the μ }(h! -space in terms of just the μ\ h jhhh!NhNubj)}(h:sub:`k`h]h/k}(hhh jubah}(h]h]h]h]h]uhjh jubh/ and η }(h and η\ h jhhh!NhNubj)}(h:sub:`k`h]h/k}(hhh jubah}(h]h]h]h]h]uhjh jubh/(
components of the discrete directions }(h(
components of the discrete directions h jhhh!NhNubjY)}(hjKh]h/
\Omega_{k}}(hhh j2hhh!NhNubah}(h]h]h]h]h]uhjXh!NhNh jhhubh/. One must recognize, however,
that the length of the path traveled by particles moving in a direction
out of the x-y plane is always longer than the x-y projection of the
path, by a factor of (μ }(h. One must recognize, however,
that the length of the path traveled by particles moving in a direction
out of the x-y plane is always longer than the x-y projection of the
path, by a factor of (μ\ h jhhh!NhNubjY)}(h:sup:`2`h]h/2}(hhh jDubah}(h]h]h]h]h]uhjXh jubh/ + η }(h + η\ h jhhh!NhNubjY)}(h:sup:`2`h]h/2}(hhh jWubah}(h]h]h]h]h]uhjXh jubh/) }(h)\ h jhhh!NhNubjY)}(h
:sup:`–1/2`h]h/–1/2}(hhh jjubah}(h]h]h]h]h]uhjXh jubh/. Thus, for any
path length }(h. Thus, for any
path length h jhhh!NhNubj)}(h*s*h]h/s}(hhh j}ubah}(h]h]h]h]h]uhjh jubh/7’ measured in the x‑y plane for a given direction }(h5' measured in the x‑y plane for a given direction h jhhh!NhNubjY)}(hjKh]h/
\Omega_{k}}(hhh jhhh!NhNubah}(h]h]h]h]h]uhjXh!NhNh jhhubh/#, the
true path length traveled is }(h#, the
true path length traveled is h jhhh!NhNubj)}(h*s*h]h/s}(hhh jubah}(h]h]h]h]h]uhjh jubh/, where}(h, whereh jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-21uhh
h jhhh!h"hNubj))}(h.s=\frac{s^{\prime}}{\sqrt{\mu^{2}+\eta^{2}}} .h]h/.s=\frac{s^{\prime}}{\sqrt{\mu^{2}+\eta^{2}}} .}(hhh jubah}(h]jah]h]h]h]docnamehjnumberKlabeleq9-2-21nowrapj=j>uhj(h!h"hMh jhhj}j}jjsubhM)}(h*This is illustrated in :numref:`fig9-2-5`.h](h/This is illustrated in }(hThis is illustrated in h jhhh!NhNubj)}(h:numref:`fig9-2-5`h]jM)}(hjh]h/fig9-2-5}(hhh jubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjreftypenumrefrefexplicitrefwarnjWfig9-2-5uhjh!h"hMh jubh/.}(hhh jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jhhubh)}(h
.. _fig9-2-5:h]h}(h]h]h]h]h]hfig9-2-5uhh
hMh jhhh!h"ubj)}(hhh](j)}(h.. figure:: figs/NEWT/fig5.png
:align: center
:width: 500
Relationship between *s*\ :sub:`1` and *s*\ :sub:`2` and
their projections in the x-y plane.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig5.pngj*}j,j(suhjh jh!h"hMubj.)}(h\Relationship between *s*\ :sub:`1` and *s*\ :sub:`2` and
their projections in the x-y plane.h](h/Relationship between }(hRelationship between h j*ubj)}(h*s*h]h/s}(hhh j3ubah}(h]h]h]h]h]uhjh j*ubh/ }(h\ h j*ubj)}(h:sub:`1`h]h/1}(hhh jFubah}(h]h]h]h]h]uhjh j*ubh/ and }(h and h j*ubj)}(h*s*h]h/s}(hhh jYubah}(h]h]h]h]h]uhjh j*ubh/ }(hjEh j*ubj)}(h:sub:`2`h]h/2}(hhh jkubah}(h]h]h]h]h]uhjh j*ubh/( and
their projections in the x-y plane.}(h( and
their projections in the x-y plane.h j*ubeh}(h]h]h]h]h]uhj-h!h"hMh jubeh}(h](id163jeh]h]fig9-2-5ah]h]jEcenteruhjhMh jhhh!h"j}jj
sj}jj
subh)}(h.. _9-2-2-3-6:h]h}(h]h]h]h]h]hid35uhh
hMh jhhh!h"ubeh}(h](Gmapping-a-characteristic-vector-into-the-two-dimensional-problem-domainjeh]h](Gmapping a characteristic vector into the two-dimensional problem domain 9-2-2-3-5eh]h]uhh#h j_hhh!h"hMj}jjsj}jjsubh$)}(hhh](h))}(h+Neutron balance within a computational cellh]h/+Neutron balance within a computational cell}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hMubhM)}(hX]Once angular fluxes have been computed for all sides of a cell, it is
necessary to compute the cell-averaged angular flux. To enforce
conservation, a balance condition is applied to the cell. This provides
the equation necessary to determine the average flux in the cell. The
neutron balance for an arbitrary cell in steady state may be expressed
ash]h/X]Once angular fluxes have been computed for all sides of a cell, it is
necessary to compute the cell-averaged angular flux. To enforce
conservation, a balance condition is applied to the cell. This provides
the equation necessary to determine the average flux in the cell. The
neutron balance for an arbitrary cell in steady state may be expressed
as}(hjh jhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-22uhh
h jhhh!h"hNubj))}(hX
\left[\begin{array}{c}
\text { net number of } \\
\text { neutrons moving in } \\
\text { direction } \hat{\Omega} \text { escaping } \\
\text { from the cell }
\end{array}\right]+\left[\begin{array}{c}
\text { number of neutrons } \\
\text { removed from the cell } \\
\text { or from direction } \hat{\Omega} \\
\text { by interactions }
\end{array}\right]=\left[\begin{array}{c}
\text { number of } \\
\text { neutrons produced } \\
\text { in the cell moving } \\
\text { in direction } \hat{\Omega}
\end{array}\right]h]h/X
\left[\begin{array}{c}
\text { net number of } \\
\text { neutrons moving in } \\
\text { direction } \hat{\Omega} \text { escaping } \\
\text { from the cell }
\end{array}\right]+\left[\begin{array}{c}
\text { number of neutrons } \\
\text { removed from the cell } \\
\text { or from direction } \hat{\Omega} \\
\text { by interactions }
\end{array}\right]=\left[\begin{array}{c}
\text { number of } \\
\text { neutrons produced } \\
\text { in the cell moving } \\
\text { in direction } \hat{\Omega}
\end{array}\right]}(hhh jubah}(h]jah]h]h]h]docnamehjnumberKlabeleq9-2-22nowrapj=j>uhj(h!h"hMh jhhj}j}jjsubhM)}(hor, expressed mathematically,h]h/or, expressed mathematically,}(hjh jhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-23uhh
h jhhh!h"hNubj))}(hH\oint_{s} n \cdot \hat{\Omega}_{k} \psi d S+\sigma_{t} \bar{\psi} V=Q V,h]h/H\oint_{s} n \cdot \hat{\Omega}_{k} \psi d S+\sigma_{t} \bar{\psi} V=Q V,}(hhh jubah}(h]jah]h]h]h]docnamehjnumberKlabeleq9-2-23nowrapj=j>uhj(h!h"hMh jhhj}j}jjsubhM)}(hXewhere :math:`n` is the outward normal direction at each side of the cell and V is
the 2-D volume of the cell. Note that in this context, *S* represents
the surface area or perimeter of the cell. Hence, for a cell with *m*
sides, each of the sides having a constant angular flux :math:`\bar{\psi}_{i}` and an outward
normal direction :math:`\mathrm{n}_{i}`,h](h/where }(hwhere h jhhh!NhNubjY)}(h :math:`n`h]h/n}(hhh jubah}(h]h]h]h]h]uhjXh jubh/z is the outward normal direction at each side of the cell and V is
the 2-D volume of the cell. Note that in this context, }(hz is the outward normal direction at each side of the cell and V is
the 2-D volume of the cell. Note that in this context, h jhhh!NhNubj)}(h*S*h]h/S}(hhh j,ubah}(h]h]h]h]h]uhjh jubh/N represents
the surface area or perimeter of the cell. Hence, for a cell with }(hN represents
the surface area or perimeter of the cell. Hence, for a cell with h jhhh!NhNubj)}(h*m*h]h/m}(hhh j?ubah}(h]h]h]h]h]uhjh jubh/9
sides, each of the sides having a constant angular flux }(h9
sides, each of the sides having a constant angular flux h jhhh!NhNubjY)}(h:math:`\bar{\psi}_{i}`h]h/\bar{\psi}_{i}}(hhh jRubah}(h]h]h]h]h]uhjXh jubh/" and an outward
normal direction }(h" and an outward
normal direction h jhhh!NhNubjY)}(h:math:`\mathrm{n}_{i}`h]h/\mathrm{n}_{i}}(hhh jeubah}(h]h]h]h]h]uhjXh jubh/,}(hjzh jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-24uhh
h jhhh!h"hNubj))}(h\bar{\psi}_{c e l l}=\frac{Q}{\sigma_{t}}-\frac{1}{\sigma_{t} V} \sum_{i=1}^{m} \bar{\psi}_{i} \int_{S_{i}} \mathrm{n}_{i} \cdot \hat{\Omega}_{k} d S_{i} .h]h/\bar{\psi}_{c e l l}=\frac{Q}{\sigma_{t}}-\frac{1}{\sigma_{t} V} \sum_{i=1}^{m} \bar{\psi}_{i} \int_{S_{i}} \mathrm{n}_{i} \cdot \hat{\Omega}_{k} d S_{i} .}(hhh jubah}(h]jah]h]h]h]docnamehjnumberKlabeleq9-2-24nowrapj=j>uhj(h!h"hMh jhhj}j}jj}subhM)}(hBecause each cell is restricted to be a polygon, each side in the cell
will be a straight line and :math:`\mathrm{n}_{i} \cdot \hat{\Omega}_{k}` will be constant along the length of the
side. Equation :eq:`eq9-2-24` can then be simplified to obtainh](h/cBecause each cell is restricted to be a polygon, each side in the cell
will be a straight line and }(hcBecause each cell is restricted to be a polygon, each side in the cell
will be a straight line and h jhhh!NhNubjY)}(h-:math:`\mathrm{n}_{i} \cdot \hat{\Omega}_{k}`h]h/%\mathrm{n}_{i} \cdot \hat{\Omega}_{k}}(hhh jubah}(h]h]h]h]h]uhjXh jubh/: will be constant along the length of the
side. Equation }(h: will be constant along the length of the
side. Equation h jhhh!NhNubj)}(h:eq:`eq9-2-24`h]jM)}(hjh]h/eq9-2-24}(hhh jubah}(h]h](jEeqeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjXreftypejrefexplicitrefwarnjWeq9-2-24uhjh!h"hMh jubh/! can then be simplified to obtain}(h! can then be simplified to obtainh jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-25uhh
h jhhh!h"hNubj))}(h\bar{\psi}_{c e l l}=\frac{Q}{\sigma_{t}}-\frac{1}{\sigma_{t} V} \sum_{i=1}^{m} \bar{\psi}_{i}\left(\mathrm{n}_{i} \cdot \hat{\Omega}_{k} \mathrm{~L}_{i}\right) ,h]h/\bar{\psi}_{c e l l}=\frac{Q}{\sigma_{t}}-\frac{1}{\sigma_{t} V} \sum_{i=1}^{m} \bar{\psi}_{i}\left(\mathrm{n}_{i} \cdot \hat{\Omega}_{k} \mathrm{~L}_{i}\right) ,}(hhh jubah}(h]jah]h]h]h]docnamehjnumberKlabeleq9-2-25nowrapj=j>uhj(h!h"hMh jhhj}j}jjsubhM)}(hwhere L\ :sub:`i` is the length of the *i*\ th side and the term in
parentheses represents a leakage coefficient for the side.h](h/ where L }(h where L\ h jhhh!NhNubj)}(h:sub:`i`h]h/i}(hhh j ubah}(h]h]h]h]h]uhjh jubh/ is the length of the }(h is the length of the h jhhh!NhNubj)}(h*i*h]h/i}(hhh jubah}(h]h]h]h]h]uhjh jubh/U th side and the term in
parentheses represents a leakage coefficient for the side.}(hU\ th side and the term in
parentheses represents a leakage coefficient for the side.h jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM h jhhubh)}(h.. _9-2-2-4:h]h}(h]h]h]h]h]hid36uhh
hM#h jhhh!h"ubeh}(h](+neutron-balance-within-a-computational-celljeh]h](+neutron balance within a computational cell 9-2-2-3-6eh]h]uhh#h j_hhh!h"hMj}jFjsj}jjsubeh}(h]()the-extended-step-characteristic-approachjSeh]h]()the extended step characteristic approach9-2-2-3eh]h]uhh#h jhhh!h"hM|j}jQjIsj}jSjIsubh$)}(hhh](h))}(h*Coarse-mesh finite-difference accelerationh]h/*Coarse-mesh finite-difference acceleration}(hj[h jYhhh!NhNubah}(h]h]h]h]h]uhh(h jVhhh!h"hM&ubhM)}(hX*Beyond cell discretization and solution described above for the ESC
approach, the NEWT iterative approach is similar to that used in other
discrete-ordinates methods. Inner iterations are used to solve spatial
fluxes in each energy group to generate updated source terms; outer
iterations use these source terms to converge all energy groups. This
source-iteration approach can be somewhat slow to converge, especially
when significant scattering is present. Hence, it is desirable to apply
some form of acceleration to the iterative solution used by NEWT. To
this end, a coarse-mesh finite-difference acceleration (CMFD) approach
has been added to NEWT. The CMFD formulation uses a simplified
representation of a complex problem, in which selected rectangular
regions are derived from the global NEWT Cartesian grid and homogenized.
The CMFD formulation utilizes coupling correction factors for each
homogenized cell to dynamically homogenize the constituent ESC-based
polygonal cells during the iterative solution process such that the
heterogeneous transport solution can be preserved. Dynamic-group
collapse is also possible with a two-level CMFD formulation in which
alternating multigroup and two-group calculations are performed. By
extending the concept of the equivalence theory to energy and angle, it
is possible to apply a consistent lower-order formulation in the form of
a homogenized pin-cell, few-group, diffusion-like finite-difference
scheme. This simplified lower-order formulation is much less expensive
to solve, and its solution can be used to accelerate the original
higher-order transport solution in NEWT, resulting in much faster
convergence of the fission and scattering source distributions. This
work is described in detail in :cite:`zhong_implementation_2008` and in previous versions of
the NEWT manual.h](h/XBeyond cell discretization and solution described above for the ESC
approach, the NEWT iterative approach is similar to that used in other
discrete-ordinates methods. Inner iterations are used to solve spatial
fluxes in each energy group to generate updated source terms; outer
iterations use these source terms to converge all energy groups. This
source-iteration approach can be somewhat slow to converge, especially
when significant scattering is present. Hence, it is desirable to apply
some form of acceleration to the iterative solution used by NEWT. To
this end, a coarse-mesh finite-difference acceleration (CMFD) approach
has been added to NEWT. The CMFD formulation uses a simplified
representation of a complex problem, in which selected rectangular
regions are derived from the global NEWT Cartesian grid and homogenized.
The CMFD formulation utilizes coupling correction factors for each
homogenized cell to dynamically homogenize the constituent ESC-based
polygonal cells during the iterative solution process such that the
heterogeneous transport solution can be preserved. Dynamic-group
collapse is also possible with a two-level CMFD formulation in which
alternating multigroup and two-group calculations are performed. By
extending the concept of the equivalence theory to energy and angle, it
is possible to apply a consistent lower-order formulation in the form of
a homogenized pin-cell, few-group, diffusion-like finite-difference
scheme. This simplified lower-order formulation is much less expensive
to solve, and its solution can be used to accelerate the original
higher-order transport solution in NEWT, resulting in much faster
convergence of the fission and scattering source distributions. This
work is described in detail in }(hXBeyond cell discretization and solution described above for the ESC
approach, the NEWT iterative approach is similar to that used in other
discrete-ordinates methods. Inner iterations are used to solve spatial
fluxes in each energy group to generate updated source terms; outer
iterations use these source terms to converge all energy groups. This
source-iteration approach can be somewhat slow to converge, especially
when significant scattering is present. Hence, it is desirable to apply
some form of acceleration to the iterative solution used by NEWT. To
this end, a coarse-mesh finite-difference acceleration (CMFD) approach
has been added to NEWT. The CMFD formulation uses a simplified
representation of a complex problem, in which selected rectangular
regions are derived from the global NEWT Cartesian grid and homogenized.
The CMFD formulation utilizes coupling correction factors for each
homogenized cell to dynamically homogenize the constituent ESC-based
polygonal cells during the iterative solution process such that the
heterogeneous transport solution can be preserved. Dynamic-group
collapse is also possible with a two-level CMFD formulation in which
alternating multigroup and two-group calculations are performed. By
extending the concept of the equivalence theory to energy and angle, it
is possible to apply a consistent lower-order formulation in the form of
a homogenized pin-cell, few-group, diffusion-like finite-difference
scheme. This simplified lower-order formulation is much less expensive
to solve, and its solution can be used to accelerate the original
higher-order transport solution in NEWT, resulting in much faster
convergence of the fission and scattering source distributions. This
work is described in detail in h jghhh!NhNubj)}(hzhong_implementation_2008h]j)}(hjrh]h/[zhong_implementation_2008]}(hhh jtubah}(h]h]h]h]h]uhjh jpubah}(h]id37ah]jah]h]h] refdomainjreftypej reftargetjrrefwarnsupport_smartquotesuhjh!h"hM(h jghhubh/- and in previous versions of
the NEWT manual.}(h- and in previous versions of
the NEWT manual.h jghhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM(h jVhhubhM)}(hXLAlthough the original implementation of the CMFD acceleration method is
extremely efficient and actively maintained, its use is limited to
rectangular-domain configurations (e.g., square-pitched fuel lattices).
An alternative CMFD acceleration method has been developed to support
triangular- and hexagonal-domain configurations (e.g.,
triangular-pitched fuel lattices such as the VVER or prismatic graphite
models). The new CMFD acceleration method does not require the
coarse-mesh cells to be rectangles but rather arbitrary polygons.
However in the current implementation, the “unstructured” coarse-mesh
cells are still constructed from the global NEWT Cartesian grid.
Therefore, for a hexagonal configuration, interior coarse-mesh cells
will be rectangular shape whereas cells near the boundary will be
triangular or trapezoidal shapes.h]h/XLAlthough the original implementation of the CMFD acceleration method is
extremely efficient and actively maintained, its use is limited to
rectangular-domain configurations (e.g., square-pitched fuel lattices).
An alternative CMFD acceleration method has been developed to support
triangular- and hexagonal-domain configurations (e.g.,
triangular-pitched fuel lattices such as the VVER or prismatic graphite
models). The new CMFD acceleration method does not require the
coarse-mesh cells to be rectangles but rather arbitrary polygons.
However in the current implementation, the “unstructured” coarse-mesh
cells are still constructed from the global NEWT Cartesian grid.
Therefore, for a hexagonal configuration, interior coarse-mesh cells
will be rectangular shape whereas cells near the boundary will be
triangular or trapezoidal shapes.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMDh jVhhubhM)}(hXPThe new unstructured CMFD iterative solution scheme is essentially
identical to the original solution scheme; the two methods differ only
in how the lower-order system is solved. Additionally the two-group
acceleration is not employed in the unstructured CMFD method. Input
options for both CMFD methods are described in :ref:`9-2-3-2`.h](h/XAThe new unstructured CMFD iterative solution scheme is essentially
identical to the original solution scheme; the two methods differ only
in how the lower-order system is solved. Additionally the two-group
acceleration is not employed in the unstructured CMFD method. Input
options for both CMFD methods are described in }(hXAThe new unstructured CMFD iterative solution scheme is essentially
identical to the original solution scheme; the two methods differ only
in how the lower-order system is solved. Additionally the two-group
acceleration is not employed in the unstructured CMFD method. Input
options for both CMFD methods are described in h jhhh!NhNubj)}(h:ref:`9-2-3-2`h]j)}(hjh]h/9-2-3-2}(hhh jubah}(h]h](jEstdstd-refeh]h]h]uhjh jubah}(h]h]h]h]h]refdochj refdomainjreftyperefrefexplicitrefwarnjW9-2-3-2uhjh!h"hMRh jubh/.}(hhh jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMRh jVhhubh)}(h.. _9-2-2-5:h]h}(h]h]h]h]h]hid38uhh
hMXh jVhhh!h"ubeh}(h](*coarse-mesh-finite-difference-accelerationj?eh]h](*coarse-mesh finite-difference acceleration9-2-2-4eh]h]uhh#h jhhh!h"hM&j}jj5sj}j?j5subh$)}(hhh](h))}(hAssembly discontinuity factorsh]h/Assembly discontinuity factors}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hM[ubhM)}(hX
In nodal multi-assembly or core calculations, lattice transport
solutions are used to generate few-group homogenized cross sections.
These cross sections are in general obtained from single-assembly
transport calculations with zero-current boundary conditions. Generation
of few-group homogenized cross sections for nodal calculations typically
includes the generation of discontinuity factors (i.e., additional
parameters used to preserve both reaction rates and the interface
currents in the homogenization process). The discontinuity of the flux
at an assembly interface that can arise by the use of homogenized
cross sections is illustrated in :numref:`fig9-2-6`. The so-called
“homogeneous” flux, computed in the nodal calculation, is discontinuous
at the assembly interface, as opposed to the exact “heterogeneous” flux,
computed in the transport calculation, which is continuous at the
assembly interface. The interface condition employed in nodal
calculations between two assemblies (nodes) *i* and *i*\ +1 is given ash](h/XIn nodal multi-assembly or core calculations, lattice transport
solutions are used to generate few-group homogenized cross sections.
These cross sections are in general obtained from single-assembly
transport calculations with zero-current boundary conditions. Generation
of few-group homogenized cross sections for nodal calculations typically
includes the generation of discontinuity factors (i.e., additional
parameters used to preserve both reaction rates and the interface
currents in the homogenization process). The discontinuity of the flux
at an assembly interface that can arise by the use of homogenized
cross sections is illustrated in }(hXIn nodal multi-assembly or core calculations, lattice transport
solutions are used to generate few-group homogenized cross sections.
These cross sections are in general obtained from single-assembly
transport calculations with zero-current boundary conditions. Generation
of few-group homogenized cross sections for nodal calculations typically
includes the generation of discontinuity factors (i.e., additional
parameters used to preserve both reaction rates and the interface
currents in the homogenization process). The discontinuity of the flux
at an assembly interface that can arise by the use of homogenized
cross sections is illustrated in h jhhh!NhNubj)}(h:numref:`fig9-2-6`h]jM)}(hjh]h/fig9-2-6}(hhh j
ubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh j ubah}(h]h]h]h]h]refdochj refdomainjreftypenumrefrefexplicitrefwarnjWfig9-2-6uhjh!h"hM^h jubh/XU. The so-called
“homogeneous” flux, computed in the nodal calculation, is discontinuous
at the assembly interface, as opposed to the exact “heterogeneous” flux,
computed in the transport calculation, which is continuous at the
assembly interface. The interface condition employed in nodal
calculations between two assemblies (nodes) }(hXU. The so-called
“homogeneous” flux, computed in the nodal calculation, is discontinuous
at the assembly interface, as opposed to the exact “heterogeneous” flux,
computed in the transport calculation, which is continuous at the
assembly interface. The interface condition employed in nodal
calculations between two assemblies (nodes) h jhhh!NhNubj)}(h*i*h]h/i}(hhh j.ubah}(h]h]h]h]h]uhjh jubh/ and }(h and h jhhh!NhNubj)}(h*i*h]h/i}(hhh jAubah}(h]h]h]h]h]uhjh jubh/ +1 is given as}(h\ +1 is given ash jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM^h jhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-26uhh
h jhhh!h"hNubj))}(hm\phi_{i, \text { homogeneous }}^{+} \cdot F_{i}^{+}=\phi_{i+1, \text { homogeneous }}^{-} \cdot F_{i+1}^{-} ,h]h/m\phi_{i, \text { homogeneous }}^{+} \cdot F_{i}^{+}=\phi_{i+1, \text { homogeneous }}^{-} \cdot F_{i+1}^{-} ,}(hhh jdubah}(h]jcah]h]h]h]docnamehjnumberKlabeleq9-2-26nowrapj=j>uhj(h!h"hMnh jhhj}j}jcjZsubhM)}(hwhere :math:`F_{i}^{+}` and :math:`F_{i+1}^{-}` are assembly discontinuity factors (ADFs) on each side of the
interface between assemblies *i* and *i*\ +1.h](h/where }(hwhere h jyhhh!NhNubjY)}(h:math:`F_{i}^{+}`h]h/ F_{i}^{+}}(hhh jubah}(h]h]h]h]h]uhjXh jyubh/ and }(h and h jyhhh!NhNubjY)}(h:math:`F_{i+1}^{-}`h]h/F_{i+1}^{-}}(hhh jubah}(h]h]h]h]h]uhjXh jyubh/\ are assembly discontinuity factors (ADFs) on each side of the
interface between assemblies }(h\ are assembly discontinuity factors (ADFs) on each side of the
interface between assemblies h jyhhh!NhNubj)}(h*i*h]h/i}(hhh jubah}(h]h]h]h]h]uhjh jyubh/ and }(hjh jyubj)}(h*i*h]h/i}(hhh jubah}(h]h]h]h]h]uhjh jyubh/ +1.}(h\ +1.h jyhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMsh jhhubhM)}(hX1The ADF on the assembly interface is defined as the ratio of the
heterogeneous flux :math:`\phi_{\text {heterogeneous }}` at that assembly interface to the homogeneous flux
evaluated at the interface, denoted :math:`\phi_{i, \text { homogeneous }}^{+}` (or :math:`\phi_{i+1, \text { homogeneous }}^{-}`):h](h/TThe ADF on the assembly interface is defined as the ratio of the
heterogeneous flux }(hTThe ADF on the assembly interface is defined as the ratio of the
heterogeneous flux h jhhh!NhNubjY)}(h%:math:`\phi_{\text {heterogeneous }}`h]h/\phi_{\text {heterogeneous }}}(hhh jubah}(h]h]h]h]h]uhjXh jubh/X at that assembly interface to the homogeneous flux
evaluated at the interface, denoted }(hX at that assembly interface to the homogeneous flux
evaluated at the interface, denoted h jhhh!NhNubjY)}(h+:math:`\phi_{i, \text { homogeneous }}^{+}`h]h/#\phi_{i, \text { homogeneous }}^{+}}(hhh jubah}(h]h]h]h]h]uhjXh jubh/ (or }(h (or h jhhh!NhNubjY)}(h-:math:`\phi_{i+1, \text { homogeneous }}^{-}`h]h/%\phi_{i+1, \text { homogeneous }}^{-}}(hhh jubah}(h]h]h]h]h]uhjXh jubh/):}(h):h jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMvh jhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-27uhh
h jhhh!h"hNubj))}(hF_{i}^{+}=\frac{\phi_{\text {heterogeneous }}}{\phi_{i, \text { homogeneous }}^{+}}, F_{i+1}^{-}=\frac{\phi_{\text {heterogeneous }}}{\phi_{i+1, \text { homogeneous }}^{-}} .h]h/F_{i}^{+}=\frac{\phi_{\text {heterogeneous }}}{\phi_{i, \text { homogeneous }}^{+}}, F_{i+1}^{-}=\frac{\phi_{\text {heterogeneous }}}{\phi_{i+1, \text { homogeneous }}^{-}} .}(hhh j%ubah}(h]j$ah]h]h]h]docnamehjnumberKlabeleq9-2-27nowrapj=j>uhj(h!h"hMzh jhhj}j}j$jsubhM)}(hFluxes, and therefore ADFs, vary with energy; therefore, few-group
homogenized cross sections are always accompanied by corresponding
few-group ADFs.h]h/Fluxes, and therefore ADFs, vary with energy; therefore, few-group
homogenized cross sections are always accompanied by corresponding
few-group ADFs.}(hj<h j:hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jhhubhM)}(hXIn a single-assembly calculation with zero-current boundary conditions,
the heterogeneous flux at each boundary is easily calculated as the
surface-averaged scalar flux on the boundary, whereas the homogenous
flux at each boundary is simply the assembly-averaged flux. Hence, for
each energy group, the ADF is calculated for each boundary as the ratio
of the average flux on that boundary to the average flux across the
assembly.h]h/XIn a single-assembly calculation with zero-current boundary conditions,
the heterogeneous flux at each boundary is easily calculated as the
surface-averaged scalar flux on the boundary, whereas the homogenous
flux at each boundary is simply the assembly-averaged flux. Hence, for
each energy group, the ADF is calculated for each boundary as the ratio
of the average flux on that boundary to the average flux across the
assembly.}(hjJh jHhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jhhubhM)}(hXIn other configurations, such as a multi-assembly calculation or an
assembly located on the edge of a core next to the core baffle and
reflector, the ADF calculation requires more effort. For reflector
situations, NEWT applies a simple one-dimensional (1-D) multigroup
diffusion approximation to determine the ADF at the assembly boundary.
In this approximation, it is assumed that the reflector is infinite and
that the scalar flux goes to zero at infinity. The reflector ADF can be
determined analytically using this boundary condition along with the
known surface-averaged current and scalar flux evaluated at the
assembly/reflector interface.h]h/XIn other configurations, such as a multi-assembly calculation or an
assembly located on the edge of a core next to the core baffle and
reflector, the ADF calculation requires more effort. For reflector
situations, NEWT applies a simple one-dimensional (1-D) multigroup
diffusion approximation to determine the ADF at the assembly boundary.
In this approximation, it is assumed that the reflector is infinite and
that the scalar flux goes to zero at infinity. The reflector ADF can be
determined analytically using this boundary condition along with the
known surface-averaged current and scalar flux evaluated at the
assembly/reflector interface.}(hjXh jVhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jhhubhM)}(hXZThe reflector ADFs computed by NEWT may potentially be different from
the ADFs calculated using the diffusion approximations employed by the
nodal code. Moreover, ADFs computed for multi-assembly or
hexagonal-domain configurations will depend on the nodal method
employed. For these reasons, NEWT supports the option to edit
surface-averaged scalar flux and current values along user-defined line
segments so that appropriate ADFs can be computed directly by the nodal
code. The input options for the single-assembly ADF, reflector ADF, and
arbitrary line-segment edit are discussed in :ref:`9-2-3-11`.h](h/XJThe reflector ADFs computed by NEWT may potentially be different from
the ADFs calculated using the diffusion approximations employed by the
nodal code. Moreover, ADFs computed for multi-assembly or
hexagonal-domain configurations will depend on the nodal method
employed. For these reasons, NEWT supports the option to edit
surface-averaged scalar flux and current values along user-defined line
segments so that appropriate ADFs can be computed directly by the nodal
code. The input options for the single-assembly ADF, reflector ADF, and
arbitrary line-segment edit are discussed in }(hXJThe reflector ADFs computed by NEWT may potentially be different from
the ADFs calculated using the diffusion approximations employed by the
nodal code. Moreover, ADFs computed for multi-assembly or
hexagonal-domain configurations will depend on the nodal method
employed. For these reasons, NEWT supports the option to edit
surface-averaged scalar flux and current values along user-defined line
segments so that appropriate ADFs can be computed directly by the nodal
code. The input options for the single-assembly ADF, reflector ADF, and
arbitrary line-segment edit are discussed in h jdhhh!NhNubj)}(h:ref:`9-2-3-11`h]j)}(hjoh]h/9-2-3-11}(hhh jqubah}(h]h](jEstdstd-refeh]h]h]uhjh jmubah}(h]h]h]h]h]refdochj refdomainj{reftyperefrefexplicitrefwarnjW9-2-3-11uhjh!h"hMh jdubh/.}(hhh jdhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jhhubh)}(h
.. _fig9-2-6:h]h}(h]h]h]h]h]hfig9-2-6uhh
hMh jhhh!h"ubj)}(hhh](j)}(h.. figure:: figs/NEWT/fig6.png
:align: center
:width: 500
Heterogeneous vs homogeneous fluxes in a multi-assembly solution.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig6.pngj*}j,jsuhjh jh!h"hMubj.)}(hAHeterogeneous vs homogeneous fluxes in a multi-assembly solution.h]h/AHeterogeneous vs homogeneous fluxes in a multi-assembly solution.}(hjh jubah}(h]h]h]h]h]uhj-h!h"hMh jubeh}(h](id164jeh]h]fig9-2-6ah]h]jEcenteruhjhMh jhhh!h"j}jjsj}jjsubh)}(h
.. _9-2-3:h]h}(h]h]h]h]h]hid39uhh
hMh jhhh!h"ubeh}(h](assembly-discontinuity-factorsjeh]h]9-2-2-5ah]assembly discontinuity factorsah]uhh#h jhhh!h"hM[
referencedKj}jjsj}jjsubeh}(h](theory-and-proceduresjeh]h](theory and procedures9-2-2eh]h]uhh#h h%hhh!h"hKj}jjsj}jjsubh$)}(hhh](h))}(h
Input Formatsh]h/
Input Formats}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hMubhM)}(hXNEWT input is free form and keyword based, similar in form to the input for many
other modules in the SCALE code package. Input may start with a title card
record, but this line may be omitted if desired; remaining data are supplied in
data blocks. The order of the data blocks is arbitrary (with two exceptions),
and many blocks are optional. Only one instance of a data block is allowed.h]h/XNEWT input is free form and keyword based, similar in form to the input for many
other modules in the SCALE code package. Input may start with a title card
record, but this line may be omitted if desired; remaining data are supplied in
data blocks. The order of the data blocks is arbitrary (with two exceptions),
and many blocks are optional. Only one instance of a data block is allowed.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jhhubh)}(h.. _9-2-3-1:h]h}(h]h]h]h]h]hid40uhh
hMh jhhh!h"ubh$)}(hhh](h))}(hOverview of newt data blocksh]h/Overview of newt data blocks}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hMubhM)}(hXThe NEWT input deck data blocks are defined by keyword delimiters in the
following form:h]h/XThe NEWT input deck data blocks are defined by keyword delimiters in the
following form:}(hj,h j*hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jhhubh
highlightlang)}(hhh]h}(h]h]h]h]h]langnoneforcelinenothresholduhj8h jhhh!h"hMubh
literal_block)}(h+read keyword [data] end keywordh]h/+read keyword [data] end keyword}(hhh jIubah}(h]h]h]h]h]j=j>uhjGh!h"hMh jhhubhM)}(hRead routines are terminated by the “end *keyword*\ ” label, and any
intervening carriage returns or line feeds are ignored. Thus, data can
also be entered in this format:h](h/+Read routines are terminated by the “end }(h+Read routines are terminated by the “end h jWhhh!NhNubj)}(h *keyword*h]h/keyword}(hhh j`ubah}(h]h]h]h]h]uhjh jWubh/{ ” label, and any
intervening carriage returns or line feeds are ignored. Thus, data can
also be entered in this format:}(h{\ ” label, and any
intervening carriage returns or line feeds are ignored. Thus, data can
also be entered in this format:h jWhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jhhubjH)}(h&read keyword
[data]
[data]
end keywordh]h/&read keyword
[data]
[data]
end keyword}(hhh jyubah}(h]h]h]h]h]j=j>uhjGh!h"hMh jhhubhM)}(hWithin each block, specific control or specification parameters are
input. Each block contains a fixed set of input parameters (also defined
by keyword).h]h/Within each block, specific control or specification parameters are
input. Each block contains a fixed set of input parameters (also defined
by keyword).}(hjh jhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jhhubhM)}(hAs with other keyword-driven modules within SCALE, lines beginning with
a single quote (') in the first column are treated as comments and
ignored.h]h/As with other keyword-driven modules within SCALE, lines beginning with
a single quote (‘) in the first column are treated as comments and
ignored.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jhhubhM)}(hHThe keyword name and general contents of each data block are as follows:h]h/HThe keyword name and general contents of each data block are as follows:}(hjh jhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jhhubh table)}(hhh]h tgroup)}(hhh](h colspec)}(hhh]h}(h]h]h]h]h]colwidthKuhjh jubj)}(hhh]h}(h]h]h]h]h]colwidthKuhjh jubj)}(hhh]h}(h]h]h]h]h]colwidthKuhjh jubh tbody)}(hhh](h row)}(hhh](h entry)}(hhh]hM)}(h**Block type**h]h)}(hjh]h/
Block type}(hhh jubah}(h]h]h]h]h]uhhh jubah}(h]h]h]h]h]uhhLh!h"hMh jubah}(h]h]h]h]h]uhjh jubj)}(hhh]hM)}(h**Recognized
keywords**h]h)}(hjh]h/Recognized
keywords}(hhh jubah}(h]h]h]h]h]uhhh j
ubah}(h]h]h]h]h]uhhLh!h"hMh jubah}(h]h]h]h]h]uhjh jubj)}(hhh]hM)}(h**Description**h]h)}(hj,h]h/Description}(hhh j.ubah}(h]h]h]h]h]uhhh j*ubah}(h]h]h]h]h]uhhLh!h"hMh j'ubah}(h]h]h]h]h]uhjh jubeh}(h]h]h]h]h]uhjh jubj)}(hhh](j)}(hhh](hM)}(hProblem control
parametersh]h/Problem control
parameters}(hjUh jSubah}(h]h]h]h]h]uhhLh!h"hMh jPubhM)}(h:ref:`9-2-3-2`h]j)}(hjch]j)}(hjch]h/9-2-3-2}(hhh jhubah}(h]h](jEstdstd-refeh]h]h]uhjh jeubah}(h]h]h]h]h]refdochj refdomainjrreftyperefrefexplicitrefwarnjW9-2-3-2uhjh!h"hMh jaubah}(h]h]h]h]h]uhhLh!h"hMh jPubeh}(h]h]h]h]h]uhjh jMubj)}(hhh]hM)}(h(parameter,
parameters, param,
parm, parah]h/(parameter,
parameters, param,
parm, para}(hjh jubah}(h]h]h]h]h]uhhLh!h"hMh jubah}(h]h]h]h]h]uhjh jMubj)}(hhh]hM)}(hGGeneral problem
parameters—must
follow title card, if
used (optional)h]h/GGeneral problem
parameters—must
follow title card, if
used (optional)}(hjh jubah}(h]h]h]h]h]uhhLh!h"hMh jubah}(h]h]h]h]h]uhjh jMubeh}(h]h]h]h]h]uhjh jubj)}(hhh](j)}(hhh](hM)}(hMaterial propertiesh]h/Material properties}(hjh jubah}(h]h]h]h]h]uhhLh!h"hMh jubhM)}(h:ref:`9-2-3-3`h]j)}(hjh]j)}(hjh]h/9-2-3-3}(hhh jubah}(h]h](jEstdstd-refeh]h]h]uhjh jubah}(h]h]h]h]h]refdochj refdomainjreftyperefrefexplicitrefwarnjW9-2-3-3uhjh!h"hMh jubah}(h]h]h]h]h]uhhLh!h"hMh jubeh}(h]h]h]h]h]uhjh jubj)}(hhh]hM)}(hmaterial, materials,
matlh]h/material, materials,
matl}(hj h j
ubah}(h]h]h]h]h]uhhLh!h"hMh j ubah}(h]h]h]h]h]uhjh jubj)}(hhh]hM)}(hAssigns
characteristics
(e.g., P\ :sub:`n`
scattering order and
material description)
for each material
ID—must follow
problem control block
or must follow title
card if control block
is omitted (required)h](h/"Assigns
characteristics
(e.g., P }(h"Assigns
characteristics
(e.g., P\ h j! ubj)}(h:sub:`n`h]h/n}(hhh j* ubah}(h]h]h]h]h]uhjh j! ubh/
scattering order and
material description)
for each material
ID—must follow
problem control block
or must follow title
card if control block
is omitted (required)}(h
scattering order and
material description)
for each material
ID—must follow
problem control block
or must follow title
card if control block
is omitted (required)h j! ubeh}(h]h]h]h]h]uhhLh!h"hMh j ubah}(h]h]h]h]h]uhjh jubeh}(h]h]h]h]h]uhjh jubj)}(hhh](j)}(hhh](hM)}(hBroad group collapseh]h/Broad group collapse}(hjW h jU ubah}(h]h]h]h]h]uhhLh!h"hMh jR ubhM)}(h:ref:`9-2-3-5`h]j)}(hje h]j)}(hje h]h/9-2-3-5}(hhh jj ubah}(h]h](jEstdstd-refeh]h]h]uhjh jg ubah}(h]h]h]h]h]refdochj refdomainjt reftyperefrefexplicitrefwarnjW9-2-3-5uhjh!h"hMh jc ubah}(h]h]h]h]h]uhhLh!h"hMh jR ubeh}(h]h]h]h]h]uhjh jO ubj)}(hhh]hM)}(hcollapse, collh]h/collapse, coll}(hj h j ubah}(h]h]h]h]h]uhhLh!h"hMh j ubah}(h]h]h]h]h]uhjh jO ubj)}(hhh]hM)}(hDefines broad group
energy ranges to be
created from the
original fine group
library when cross
section collapse is
desired (optional)h]h/Defines broad group
energy ranges to be
created from the
original fine group
library when cross
section collapse is
desired (optional)}(hj h j ubah}(h]h]h]h]h]uhhLh!h"hMh j ubah}(h]h]h]h]h]uhjh jO ubeh}(h]h]h]h]h]uhjh jubj)}(hhh](j)}(hhh](hM)}(hSimple-body geometryh]h/Simple-body geometry}(hj h j ubah}(h]h]h]h]h]uhhLh!h"hMh j ubhM)}(h:ref:`9-2-3-6`h]j)}(hj h]j)}(hj h]h/9-2-3-6}(hhh j ubah}(h]h](jEstdstd-refeh]h]h]uhjh j ubah}(h]h]h]h]h]refdochj refdomainj reftyperefrefexplicitrefwarnjW9-2-3-6uhjh!h"hMh j ubah}(h]h]h]h]h]uhhLh!h"hMh j ubeh}(h]h]h]h]h]uhjh j ubj)}(hhh]hM)}(hgeometry, geomh]h/geometry, geom}(hj!h j!ubah}(h]h]h]h]h]uhhLh!h"hMh j !ubah}(h]h]h]h]h]uhjh j ubj)}(hhh]hM)}(hDefines basic grid
structure and all
bodies to be placed
within this structure
(required unless
geometry restart file
is available)h]h/Defines basic grid
structure and all
bodies to be placed
within this structure
(required unless
geometry restart file
is available)}(hj%!h j#!ubah}(h]h]h]h]h]uhhLh!h"hMh j !ubah}(h]h]h]h]h]uhjh j ubeh}(h]h]h]h]h]uhjh jubj)}(hhh](j)}(hhh](hM)}(hBoundary conditionsh]h/Boundary conditions}(hjE!h jC!ubah}(h]h]h]h]h]uhhLh!h"hMh j@!ubhM)}(h:ref:`9-2-3-7`h]j)}(hjS!h]j)}(hjS!h]h/9-2-3-7}(hhh jX!ubah}(h]h](jEstdstd-refeh]h]h]uhjh jU!ubah}(h]h]h]h]h]refdochj refdomainjb!reftyperefrefexplicitrefwarnjW9-2-3-7uhjh!h"hMh jQ!ubah}(h]h]h]h]h]uhhLh!h"hMh j@!ubeh}(h]h]h]h]h]uhjh j=!ubj)}(hhh]hM)}(hbounds, bndsh]h/bounds, bnds}(hj!h j!ubah}(h]h]h]h]h]uhhLh!h"hMh j!ubah}(h]h]h]h]h]uhjh j=!ubj)}(hhh]hM)}(h{Defines boundary
conditions to be
applied on outer
boundaries of global
unit (optional,
default is reflective
on all sides)h]h/{Defines boundary
conditions to be
applied on outer
boundaries of global
unit (optional,
default is reflective
on all sides)}(hj!h j!ubah}(h]h]h]h]h]uhhLh!h"hMh j!ubah}(h]h]h]h]h]uhjh j=!ubeh}(h]h]h]h]h]uhjh jubj)}(hhh](j)}(hhh](hM)}(hArray specificationsh]h/Array specifications}(hj!h j!ubah}(h]h]h]h]h]uhhLh!h"hMh j!ubhM)}(h:ref:`9-2-3-9`h]j)}(hj!h]j)}(hj!h]h/9-2-3-9}(hhh j!ubah}(h]h](jEstdstd-refeh]h]h]uhjh j!ubah}(h]h]h]h]h]refdochj refdomainj!reftyperefrefexplicitrefwarnjW9-2-3-9uhjh!h"hM h j!ubah}(h]h]h]h]h]uhhLh!h"hMh j!ubeh}(h]h]h]h]h]uhjh j!ubj)}(hhh]hM)}(harrayh]h/array}(hj!h j!ubah}(h]h]h]h]h]uhhLh!h"hMh j!ubah}(h]h]h]h]h]uhjh j!ubj)}(hhh]hM)}(hDefines composition
of all arrays (unit
placement within each
array). Each array
placed within the
geometry block must
be defined in the
array blockh]h/Defines composition
of all arrays (unit
placement within each
array). Each array
placed within the
geometry block must
be defined in the
array block}(hj"h j"ubah}(h]h]h]h]h]uhhLh!h"hMh j"ubah}(h]h]h]h]h]uhjh j!ubeh}(h]h]h]h]h]uhjh jubj)}(hhh](j)}(hhh](hM)}(hHomogenization
instructionsh]h/Homogenization
instructions}(hj3"h j1"ubah}(h]h]h]h]h]uhhLh!h"hMh j."ubhM)}(h:ref:`9-2-3-10`h]j)}(hjA"h]j)}(hjA"h]h/9-2-3-10}(hhh jF"ubah}(h]h](jEstdstd-refeh]h]h]uhjh jC"ubah}(h]h]h]h]h]refdochj refdomainjP"reftyperefrefexplicitrefwarnjW9-2-3-10uhjh!h"hMh j?"ubah}(h]h]h]h]h]uhhLh!h"hMh j."ubeh}(h]h]h]h]h]uhjh j+"ubj)}(hhh]hM)}(hhomog, hmog, homoh]h/homog, hmog, homo}(hjs"h jq"ubah}(h]h]h]h]h]uhhLh!h"hMh jn"ubah}(h]h]h]h]h]uhjh j+"ubj)}(hhh]hM)}(hyDefines mixtures to
be flux weighted and
homogenized in the
preparation of a
homogenized cross
section library
(optional)h]h/yDefines mixtures to
be flux weighted and
homogenized in the
preparation of a
homogenized cross
section library
(optional)}(hj"h j"ubah}(h]h]h]h]h]uhhLh!h"hMh j"ubah}(h]h]h]h]h]uhjh j+"ubeh}(h]h]h]h]h]uhjh jubj)}(hhh](j)}(hhh](hM)}(hAssembly
discontinuity factorsh]h/Assembly
discontinuity factors}(hj"h j"ubah}(h]h]h]h]h]uhhLh!h"hMh j"ubhM)}(h:ref:`9-2-3-11`h]j)}(hj"h]j)}(hj"h]h/9-2-3-11}(hhh j"ubah}(h]h](jEstdstd-refeh]h]h]uhjh j"ubah}(h]h]h]h]h]refdochj refdomainj"reftyperefrefexplicitrefwarnjW9-2-3-11uhjh!h"hMh j"ubah}(h]h]h]h]h]uhhLh!h"hMh j"ubeh}(h]h]h]h]h]uhjh j"ubj)}(hhh]hM)}(hadfh]h/adf}(hj"h j"ubah}(h]h]h]h]h]uhhLh!h"hMh j"ubah}(h]h]h]h]h]uhjh j"ubj)}(hhh]hM)}(hlAssigns type and
location of planes at
which assembly
discontinuity factors
(ADFs) are calculated
(optional)h]h/lAssigns type and
location of planes at
which assembly
discontinuity factors
(ADFs) are calculated
(optional)}(hj#h j"ubah}(h]h]h]h]h]uhhLh!h"hMh j"ubah}(h]h]h]h]h]uhjh j"ubeh}(h]h]h]h]h]uhjh jubj)}(hhh](j)}(hhh](hM)}(h
Flux planeh]h/
Flux plane}(hj!#h j#ubah}(h]h]h]h]h]uhhLh!h"hMh j#ubhM)}(h:ref:`9-2-3-12`h]j)}(hj/#h]j)}(hj/#h]h/9-2-3-12}(hhh j4#ubah}(h]h](jEstdstd-refeh]h]h]uhjh j1#ubah}(h]h]h]h]h]refdochj refdomainj>#reftyperefrefexplicitrefwarnjW9-2-3-12uhjh!h"hM!h j-#ubah}(h]h]h]h]h]uhhLh!h"hM h j#ubeh}(h]h]h]h]h]uhjh j#ubj)}(hhh]hM)}(hfluxh]h/flux}(hja#h j_#ubah}(h]h]h]h]h]uhhLh!h"hMh j\#ubah}(h]h]h]h]h]uhjh j#ubj)}(hhh]hM)}(hnAllows definition of
an x- or y-axis line
(plane) for which
average fluxes are
computed and printed
(optional)h]h/nAllows definition of
an x- or y-axis line
(plane) for which
average fluxes are
computed and printed
(optional)}(hjx#h jv#ubah}(h]h]h]h]h]uhhLh!h"hMh js#ubah}(h]h]h]h]h]uhjh j#ubeh}(h]h]h]h]h]uhjh jubj)}(hhh](j)}(hhh](hM)}(hMixing tableh]h/Mixing table}(hj#h j#ubah}(h]h]h]h]h]uhhLh!h"hM%h j#ubhM)}(h:ref:`9-2-3-13`h]j)}(hj#h]j)}(hj#h]h/9-2-3-13}(hhh j#ubah}(h]h](jEstdstd-refeh]h]h]uhjh j#ubah}(h]h]h]h]h]refdochj refdomainj#reftyperefrefexplicitrefwarnjW9-2-3-13uhjh!h"hM(h j#ubah}(h]h]h]h]h]uhhLh!h"hM'h j#ubeh}(h]h]h]h]h]uhjh j#ubj)}(hhh]hM)}(hmixtable, mixth]h/mixtable, mixt}(hj#h j#ubah}(h]h]h]h]h]uhhLh!h"hM%h j#ubah}(h]h]h]h]h]uhjh j#ubj)}(hhh]hM)}(h%Mixing table
specification
(optional)h]h/%Mixing table
specification
(optional)}(hj#h j#ubah}(h]h]h]h]h]uhhLh!h"hM%h j#ubah}(h]h]h]h]h]uhjh j#ubeh}(h]h]h]h]h]uhjh jubj)}(hhh](j)}(hhh](hM)}(hSource definitionh]h/Source definition}(hj$h j
$ubah}(h]h]h]h]h]uhhLh!h"hM)h j
$ubhM)}(h:ref:`9-2-3-4`h]j)}(hj$h]j)}(hj$h]h/9-2-3-4}(hhh j"$ubah}(h]h](jEstdstd-refeh]h]h]uhjh j$ubah}(h]h]h]h]h]refdochj refdomainj,$reftyperefrefexplicitrefwarnjW9-2-3-4uhjh!h"hM,h j$ubah}(h]h]h]h]h]uhhLh!h"hM+h j
$ubeh}(h]h]h]h]h]uhjh j$ubj)}(hhh]hM)}(hsrc, sourceh]h/src, source}(hjO$h jM$ubah}(h]h]h]h]h]uhhLh!h"hM)h jJ$ubah}(h]h]h]h]h]uhjh j$ubj)}(hhh]hM)}(h?Defines particle
source strength for
use in source
calculationsh]h/?Defines particle
source strength for
use in source
calculations}(hjf$h jd$ubah}(h]h]h]h]h]uhhLh!h"hM)h ja$ubah}(h]h]h]h]h]uhjh j$ubeh}(h]h]h]h]h]uhjh jubeh}(h]h]h]h]h]uhjh jubeh}(h]h]h]h]h]colsKuhjh jubah}(h]h] longtableah]h]h]jEcenteruhjh jhhh!h"hNubhM)}(hEach of the following subsections describes the parameters associated
with a specific data block, lists default values (if available), and
describes meaning of the parameter and its effect on a NEWT calculation.h]h/Each of the following subsections describes the parameters associated
with a specific data block, lists default values (if available), and
describes meaning of the parameter and its effect on a NEWT calculation.}(hj$h j$hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM/h jhhubh)}(h.. _9-2-3-2:h]h}(h]h]h]h]h]hid41uhh
hM3h jhhh!h"ubeh}(h](overview-of-newt-data-blocksjeh]h](overview of newt data blocks9-2-3-1eh]h]uhh#h jhhh!h"hMj}j$jsj}jjsubh$)}(hhh](h))}(hParameter blockh]h/Parameter block}(hj$h j$hhh!NhNubah}(h]h]h]h]h]uhh(h j$hhh!h"hM6ubhM)}(hI**Parameter Block keyword = param, parm, para, parameter, or
parameters**h]h)}(hj$h]h/EParameter Block keyword = param, parm, para, parameter, or
parameters}(hhh j$ubah}(h]h]h]h]h]uhhh j$ubah}(h]h]h]h]h]uhhLh!h"hM8h j$hhubhM)}(hXThe Parameter block contains problem control parameters and must come
immediately after the title card if one is used. Valid parameter
specifications are described below. For each keyword, allowable values
are listed in parentheses, and the default (if any) is listed in
brackets. Input that can take an arbitrary integer value is indicated by
an *IN*; similarly, any parameter that can take an arbitrary
real/floating point value is indicated by *RN* as the allowable value.
However, note that SCALE read routines do allow input of integers for
real numbers, and vice versa; the number will be converted accordingly.
The order of the parameters within the block is arbitrary, and may be
skipped if a default value is desired for that parameter. Control
parameters are set in the order in which they are input; this means that
the same parameter may be listed multiple times, but only the final
value is used.h](h/X[The Parameter block contains problem control parameters and must come
immediately after the title card if one is used. Valid parameter
specifications are described below. For each keyword, allowable values
are listed in parentheses, and the default (if any) is listed in
brackets. Input that can take an arbitrary integer value is indicated by
an }(hX[The Parameter block contains problem control parameters and must come
immediately after the title card if one is used. Valid parameter
specifications are described below. For each keyword, allowable values
are listed in parentheses, and the default (if any) is listed in
brackets. Input that can take an arbitrary integer value is indicated by
an h j$hhh!NhNubj)}(h*IN*h]h/IN}(hhh j$ubah}(h]h]h]h]h]uhjh j$ubh/`; similarly, any parameter that can take an arbitrary
real/floating point value is indicated by }(h`; similarly, any parameter that can take an arbitrary
real/floating point value is indicated by h j$hhh!NhNubj)}(h*RN*h]h/RN}(hhh j$ubah}(h]h]h]h]h]uhjh j$ubh/X as the allowable value.
However, note that SCALE read routines do allow input of integers for
real numbers, and vice versa; the number will be converted accordingly.
The order of the parameters within the block is arbitrary, and may be
skipped if a default value is desired for that parameter. Control
parameters are set in the order in which they are input; this means that
the same parameter may be listed multiple times, but only the final
value is used.}(hX as the allowable value.
However, note that SCALE read routines do allow input of integers for
real numbers, and vice versa; the number will be converted accordingly.
The order of the parameters within the block is arbitrary, and may be
skipped if a default value is desired for that parameter. Control
parameters are set in the order in which they are input; this means that
the same parameter may be listed multiple times, but only the final
value is used.h j$hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM;h j$hhubh)}(h.. _9-2-3-2-1:h]h}(h]h]h]h]h]hid42uhh
hMJh j$hhh!h"ubh$)}(hhh](h))}(h'Convergence and acceleration parametersh]h/'Convergence and acceleration parameters}(hj$%h j"%hhh!NhNubah}(h]h]h]h]h]uhh(h j%hhh!h"hMMubhM)}(hM**epseigen=**\ (*RN*) — Convergence criterion for *k*\ :sub:`eff`. [0.0001]h](h)}(h
**epseigen=**h]h/ epseigen=}(hhh j4%ubah}(h]h]h]h]h]uhhh j0%ubh/ (}(h\ (h j0%hhh!NhNubj)}(h*RN*h]h/RN}(hhh jG%ubah}(h]h]h]h]h]uhjh j0%ubh/ ) — Convergence criterion for }(h ) — Convergence criterion for h j0%hhh!NhNubj)}(h*k*h]h/k}(hhh jZ%ubah}(h]h]h]h]h]uhjh j0%ubh/ }(h\ h j0%hhh!NhNubj)}(h
:sub:`eff`h]h/eff}(hhh jm%ubah}(h]h]h]h]h]uhjh j0%ubh/
. [0.0001]}(h
. [0.0001]h j0%hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMOh j%hhubhM)}(hV**epsinner=**\ (*RN*) — Spatial convergence criterion for inner
iterations. [0.0001]h](h)}(h
**epsinner=**h]h/ epsinner=}(hhh j%ubah}(h]h]h]h]h]uhhh j%ubh/ (}(h\ (h j%hhh!NhNubj)}(h*RN*h]h/RN}(hhh j%ubah}(h]h]h]h]h]uhjh j%ubh/B) — Spatial convergence criterion for inner
iterations. [0.0001]}(hB) — Spatial convergence criterion for inner
iterations. [0.0001]h j%hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMQh j%hhubhM)}(hV**epsouter=**\ (*RN*) — Spatial convergence criterion for outer
iterations. [0.0001]h](h)}(h
**epsouter=**h]h/ epsouter=}(hhh j%ubah}(h]h]h]h]h]uhhh j%ubh/ (}(h\ (h j%hhh!NhNubj)}(h*RN*h]h/RN}(hhh j%ubah}(h]h]h]h]h]uhjh j%ubh/B) — Spatial convergence criterion for outer
iterations. [0.0001]}(hB) — Spatial convergence criterion for outer
iterations. [0.0001]h j%hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMTh j%hhubhM)}(h**epsthrm=**\ (*RN*) — Spatial convergence criterion for
thermal-upscattering iterations, if enabled. [same value as
**epsouter**]h](h)}(h**epsthrm=**h]h/epsthrm=}(hhh j%ubah}(h]h]h]h]h]uhhh j%ubh/ (}(h\ (h j%hhh!NhNubj)}(h*RN*h]h/RN}(hhh j%ubah}(h]h]h]h]h]uhjh j%ubh/d) — Spatial convergence criterion for
thermal-upscattering iterations, if enabled. [same value as
}(hd) — Spatial convergence criterion for
thermal-upscattering iterations, if enabled. [same value as
h j%hhh!NhNubh)}(h**epsouter**h]h/epsouter}(hhh j&ubah}(h]h]h]h]h]uhhh j%ubh/]}(h]h j%hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMWh j%hhubhM)}(h**epsilon=**\ (*RN*) — Simultaneously sets all (spatial and eigenvalue)
convergence criteria to the same value. [uses individual defaults]h](h)}(h**epsilon=**h]h/epsilon=}(hhh j-&ubah}(h]h]h]h]h]uhhh j)&ubh/ (}(h\ (h j)&hhh!NhNubj)}(h*RN*h]h/RN}(hhh j@&ubah}(h]h]h]h]h]uhjh j)&ubh/y) — Simultaneously sets all (spatial and eigenvalue)
convergence criteria to the same value. [uses individual defaults]}(hy) — Simultaneously sets all (spatial and eigenvalue)
convergence criteria to the same value. [uses individual defaults]h j)&hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM[h j%hhubhM)}(hX**converg**\ =(\ *cell/mix*) — Sets the region within which convergence
testing is applied. Use of *cell* will force converged scalar fluxes in
every computation cell, while *mix* will relax convergence such that
averaged scalar fluxes within a mixture are converged. The latter is
useful for mixtures in which fluxes become very small—large reflectors
or near a vacuum BC. [cell]h](h)}(h**converg**h]h/converg}(hhh j]&ubah}(h]h]h]h]h]uhhh jY&ubh/ =( }(h\ =(\ h jY&hhh!NhNubj)}(h
*cell/mix*h]h/cell/mix}(hhh jp&ubah}(h]h]h]h]h]uhjh jY&ubh/J) — Sets the region within which convergence
testing is applied. Use of }(hJ) — Sets the region within which convergence
testing is applied. Use of h jY&hhh!NhNubj)}(h*cell*h]h/cell}(hhh j&ubah}(h]h]h]h]h]uhjh jY&ubh/E will force converged scalar fluxes in
every computation cell, while }(hE will force converged scalar fluxes in
every computation cell, while h jY&hhh!NhNubj)}(h*mix*h]h/mix}(hhh j&ubah}(h]h]h]h]h]uhjh jY&ubh/ will relax convergence such that
averaged scalar fluxes within a mixture are converged. The latter is
useful for mixtures in which fluxes become very small—large reflectors
or near a vacuum BC. [cell]}(h will relax convergence such that
averaged scalar fluxes within a mixture are converged. The latter is
useful for mixtures in which fluxes become very small—large reflectors
or near a vacuum BC. [cell]h jY&hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM^h j%hhubhM)}(hT**therm**\ =(\ *yes/no*) — Enables/disables thermal-upscattering
iterations. [yes]h](h)}(h **therm**h]h/therm}(hhh j&ubah}(h]h]h]h]h]uhhh j&ubh/ =( }(h\ =(\ h j&hhh!NhNubj)}(h*yes/no*h]h/yes/no}(hhh j&ubah}(h]h]h]h]h]uhjh j&ubh/=) — Enables/disables thermal-upscattering
iterations. [yes]}(h=) — Enables/disables thermal-upscattering
iterations. [yes]h j&hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMeh j%hhubhM)}(hR**inners=**\ (*IN*) — Maximum number of inner iterations in an energy
group. [5]h](h)}(h**inners=**h]h/inners=}(hhh j&ubah}(h]h]h]h]h]uhhh j&ubh/ (}(h\ (h j&hhh!NhNubj)}(h*IN*h]h/IN}(hhh j&ubah}(h]h]h]h]h]uhjh j&ubh/@) — Maximum number of inner iterations in an energy
group. [5]}(h@) — Maximum number of inner iterations in an energy
group. [5]h j&hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMhh j%hhubhM)}(hZ**therms=**\ (*IN*) — Maximum number of thermal-upscattering iterations,
if enabled. [2]h](h)}(h**therms=**h]h/therms=}(hhh j'ubah}(h]h]h]h]h]uhhh j'ubh/ (}(h\ (h j'hhh!NhNubj)}(h*IN*h]h/IN}(hhh j&'ubah}(h]h]h]h]h]uhjh j'ubh/H) — Maximum number of thermal-upscattering iterations,
if enabled. [2]}(hH) — Maximum number of thermal-upscattering iterations,
if enabled. [2]h j'hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMkh j%hhubhM)}(h**outers=**\ (*IN*) — Maximum number of outer iterations. NEWT will stop
with an error code if more than *outers* outer iterations are required
for convergence. [250]h](h)}(h**outers=**h]h/outers=}(hhh jC'ubah}(h]h]h]h]h]uhhh j?'ubh/ (}(h\ (h j?'hhh!NhNubj)}(h*IN*h]h/IN}(hhh jV'ubah}(h]h]h]h]h]uhjh j?'ubh/Y) — Maximum number of outer iterations. NEWT will stop
with an error code if more than }(hY) — Maximum number of outer iterations. NEWT will stop
with an error code if more than h j?'hhh!NhNubj)}(h*outers*h]h/outers}(hhh ji'ubah}(h]h]h]h]h]uhjh j?'ubh/5 outer iterations are required
for convergence. [250]}(h5 outer iterations are required
for convergence. [250]h j?'hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMnh j%hhubhM)}(hX4**inrcvrg**\ =(\ *yes/no*) — If inrcvrg=yes, NEWT will continue outer
iterations until all convergence criteria are met. If inrcvrg=no, NEWT
will stop whenever outer iteration and *k*\ :sub:`eff` convergence criterion
are met, regardless of the convergence of inner or thermal-upscattering
iterations. [no]h](h)}(h**inrcvrg**h]h/inrcvrg}(hhh j'ubah}(h]h]h]h]h]uhhh j'ubh/ =( }(h\ =(\ h j'hhh!NhNubj)}(h*yes/no*h]h/yes/no}(hhh j'ubah}(h]h]h]h]h]uhjh j'ubh/) — If inrcvrg=yes, NEWT will continue outer
iterations until all convergence criteria are met. If inrcvrg=no, NEWT
will stop whenever outer iteration and }(h) — If inrcvrg=yes, NEWT will continue outer
iterations until all convergence criteria are met. If inrcvrg=no, NEWT
will stop whenever outer iteration and h j'hhh!NhNubj)}(h*k*h]h/k}(hhh j'ubah}(h]h]h]h]h]uhjh j'ubh/ }(h\ h j'hhh!NhNubj)}(h
:sub:`eff`h]h/eff}(hhh j'ubah}(h]h]h]h]h]uhjh j'ubh/o convergence criterion
are met, regardless of the convergence of inner or thermal-upscattering
iterations. [no]}(ho convergence criterion
are met, regardless of the convergence of inner or thermal-upscattering
iterations. [no]h j'hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMrh j%hhubhM)}(hX{**cmfd=**\ (*no/rect/yes/part*) — CMFD acceleration option. If cmfd=no,
CMFD acceleration is not employed. If cmfd=rect, the CMFD method is
employed. The original NEWT CMFD method can be applied only to
rectangular-domain configurations. If cmfd=yes, the unstructured CMFD
method is employed. The new unstructured CMFD method can be applied to
rectangular-, triangular-, and hexagonal- domain configurations. If
cmfd=part, an alternative version of the unstructured CMFD method is
employed and uses a “partial-current” acceleration scheme.
Alternatively, users can use cmfd=0/1/2/3 for no, rect, yes, and part,
respectively. [no]h](h)}(h **cmfd=**h]h/cmfd=}(hhh j'ubah}(h]h]h]h]h]uhhh j'ubh/ (}(h\ (h j'hhh!NhNubj)}(h*no/rect/yes/part*h]h/no/rect/yes/part}(hhh j'ubah}(h]h]h]h]h]uhjh j'ubh/X]) — CMFD acceleration option. If cmfd=no,
CMFD acceleration is not employed. If cmfd=rect, the CMFD method is
employed. The original NEWT CMFD method can be applied only to
rectangular-domain configurations. If cmfd=yes, the unstructured CMFD
method is employed. The new unstructured CMFD method can be applied to
rectangular-, triangular-, and hexagonal- domain configurations. If
cmfd=part, an alternative version of the unstructured CMFD method is
employed and uses a “partial-current” acceleration scheme.
Alternatively, users can use cmfd=0/1/2/3 for no, rect, yes, and part,
respectively. [no]}(hX]) — CMFD acceleration option. If cmfd=no,
CMFD acceleration is not employed. If cmfd=rect, the CMFD method is
employed. The original NEWT CMFD method can be applied only to
rectangular-domain configurations. If cmfd=yes, the unstructured CMFD
method is employed. The new unstructured CMFD method can be applied to
rectangular-, triangular-, and hexagonal- domain configurations. If
cmfd=part, an alternative version of the unstructured CMFD method is
employed and uses a “partial-current” acceleration scheme.
Alternatively, users can use cmfd=0/1/2/3 for no, rect, yes, and part,
respectively. [no]h j'hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMxh j%hhubhM)}(h**cmfd2g=**\ (*yes/no*) — Enables/disables the second-level two-group
CMFD accelerator within the CMFD solver. This parameter has an effect
only when cmfd=rect is set. [yes]h](h)}(h**cmfd2g=**h]h/cmfd2g=}(hhh j(ubah}(h]h]h]h]h]uhhh j(ubh/ (}(h\ (h j(hhh!NhNubj)}(h*yes/no*h]h/yes/no}(hhh j(ubah}(h]h]h]h]h]uhjh j(ubh/) — Enables/disables the second-level two-group
CMFD accelerator within the CMFD solver. This parameter has an effect
only when cmfd=rect is set. [yes]}(h) — Enables/disables the second-level two-group
CMFD accelerator within the CMFD solver. This parameter has an effect
only when cmfd=rect is set. [yes]h j(hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j%hhubhM)}(h**accel=**\ (*yes/no*) — Enables/disables source (*k*\ :sub:`eff`)
acceleration. This parameter is automatically disabled if unstructured
CMFD is employed (cmfd=yes or cmfd=part). [yes]h](h)}(h
**accel=**h]h/accel=}(hhh j<(ubah}(h]h]h]h]h]uhhh j8(ubh/ (}(h\ (h j8(hhh!NhNubj)}(h*yes/no*h]h/yes/no}(hhh jO(ubah}(h]h]h]h]h]uhjh j8(ubh/) — Enables/disables source (}(h) — Enables/disables source (h j8(hhh!NhNubj)}(h*k*h]h/k}(hhh jb(ubah}(h]h]h]h]h]uhjh j8(ubh/ }(h\ h j8(hhh!NhNubj)}(h
:sub:`eff`h]h/eff}(hhh ju(ubah}(h]h]h]h]h]uhjh j8(ubh/x)
acceleration. This parameter is automatically disabled if unstructured
CMFD is employed (cmfd=yes or cmfd=part). [yes]}(hx)
acceleration. This parameter is automatically disabled if unstructured
CMFD is employed (cmfd=yes or cmfd=part). [yes]h j8(hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j%hhubhM)}(hX**xcmfd**\ =(\ *IN),* **ycmfd**\ =(\ *IN),* **xycmfd**\ =(\ *IN)* —
These inputs specify the number of fine-mesh cells in the global NEWT
grid per coarse-mesh cell. These options are used only when CMFD
acceleration is enabled. The parameter *xcmfd* specifies the number
fine-mesh cells per coarse-mesh cell in the x‑direction. Likewise,
*ycmfd* specifies the number of fine-mesh cells per coarse-mesh cell in
the y‑direction. The parameter *xycmfd* simultaneously sets *xcmfd* and
*ycmfd* to the same value. In a special case for rectangular-domain
configurations in which the entire domain is completely filled by a
square-type array (see :ref:`9-2-3-9`), *xycmfd=0* sets the coarse mesh
based on the size of the array elements. [1]h](h)}(h **xcmfd**h]h/xcmfd}(hhh j(ubah}(h]h]h]h]h]uhhh j(ubh/ =( }(h\ =(\ h j(hhh!NhNubj)}(h*IN),*h]h/IN),}(hhh j(ubah}(h]h]h]h]h]uhjh j(ubh/ }(h h j(hhh!NhNubh)}(h **ycmfd**h]h/ycmfd}(hhh j(ubah}(h]h]h]h]h]uhhh j(ubh/ =( }(h\ =(\ h j(ubj)}(h*IN),*h]h/IN),}(hhh j(ubah}(h]h]h]h]h]uhjh j(ubh/ }(hj(h j(ubh)}(h
**xycmfd**h]h/xycmfd}(hhh j(ubah}(h]h]h]h]h]uhhh j(ubh/ =( }(hj(h j(ubj)}(h*IN)*h]h/IN)}(hhh j(ubah}(h]h]h]h]h]uhjh j(ubh/ —
These inputs specify the number of fine-mesh cells in the global NEWT
grid per coarse-mesh cell. These options are used only when CMFD
acceleration is enabled. The parameter }(h —
These inputs specify the number of fine-mesh cells in the global NEWT
grid per coarse-mesh cell. These options are used only when CMFD
acceleration is enabled. The parameter h j(hhh!NhNubj)}(h*xcmfd*h]h/xcmfd}(hhh j)ubah}(h]h]h]h]h]uhjh j(ubh/[ specifies the number
fine-mesh cells per coarse-mesh cell in the x‑direction. Likewise,
}(h[ specifies the number
fine-mesh cells per coarse-mesh cell in the x‑direction. Likewise,
h j(hhh!NhNubj)}(h*ycmfd*h]h/ycmfd}(hhh j)ubah}(h]h]h]h]h]uhjh j(ubh/b specifies the number of fine-mesh cells per coarse-mesh cell in
the y‑direction. The parameter }(hb specifies the number of fine-mesh cells per coarse-mesh cell in
the y‑direction. The parameter h j(hhh!NhNubj)}(h*xycmfd*h]h/xycmfd}(hhh j()ubah}(h]h]h]h]h]uhjh j(ubh/ simultaneously sets }(h simultaneously sets h j(hhh!NhNubj)}(h*xcmfd*h]h/xcmfd}(hhh j;)ubah}(h]h]h]h]h]uhjh j(ubh/ and
}(h and
h j(hhh!NhNubj)}(h*ycmfd*h]h/ycmfd}(hhh jN)ubah}(h]h]h]h]h]uhjh j(ubh/ to the same value. In a special case for rectangular-domain
configurations in which the entire domain is completely filled by a
square-type array (see }(h to the same value. In a special case for rectangular-domain
configurations in which the entire domain is completely filled by a
square-type array (see h j(hhh!NhNubj)}(h:ref:`9-2-3-9`h]j)}(hjc)h]h/9-2-3-9}(hhh je)ubah}(h]h](jEstdstd-refeh]h]h]uhjh ja)ubah}(h]h]h]h]h]refdochj refdomainjo)reftyperefrefexplicitrefwarnjW9-2-3-9uhjh!h"hMh j(ubh/), }(h), h j(hhh!NhNubj)}(h
*xycmfd=0*h]h/xycmfd=0}(hhh j)ubah}(h]h]h]h]h]uhjh j(ubh/B sets the coarse mesh
based on the size of the array elements. [1]}(hB sets the coarse mesh
based on the size of the array elements. [1]h j(hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j%hhubh important)}(hXDefault convergence parameters are recommended for general analysis.
Larger convergence criteria are useful for debugging if shorter run time
is desired over solution accuracy. Smaller convergence criteria are
recommended for generating reference solutions or benchmark
calculations.
CMFD acceleration should be applied whenever possible. The CMFD method
with second-level 2-group acceleration should be applied for
rectangular-domain configurations [e.g., light water reactor (LWR)
assembly models (*\ **cmfd=rect**\ *), by default*\ **cmfd2g=yes**\ *].
The unstructured CMFD method should be applied for triangular- or
hexagonal-domain configurations (*\ **cmfd=yes**\ *). If NEWT detects an
unstable CMFD condition, a warning message is printed and NEWT continues
with CMFD disabled. NEWT may also provide a terminating error message if
improper selection of the coarse mesh is detected. Internal
investigation has shown that the coarse mesh should be approximately the
same size as the unit cell used in the model. For LWR assembly models, a
fine mesh of 4 x 4 is recommended for the square-pitched unit cell,
implying that*\ **xycmfd**\ *should be 4 only if the global unit has a
mesh. If individual meshes are used in each unit definition, then the
global unit coarse-mesh cells should be sized based on the unit cell
size and, therefore, xycmfd=1 should be used. The values
of*\ **xcmfd**\ *and*\ **ycmfd**\ *do not have to be a common factor of
the number of fine-mesh cells in a given direction (NEWT will make the
last coarse-mesh cell smaller than the other coarse-mesh cells), but it
is highly recommended.
Users can gauge solution convergence by the outer iteration edit as it
is printed to the terminal window (*\ **echo=yes**\ *, see below). One
can terminate a calculation prematurely (via the Control-C option on
most platforms) if convergence or iteration parameters need to be
modified.
The TRITON control module supports a sensitivity and uncertainty
analysis sequence TSUNAMI-2D (See TRITON chapter, section S/U Analysis
Sequences (TSUNAMI-2D, TSUNAMI-2DC)). TSUNAMI-2D calculations require
NEWT to be run in both forward mode and adjoint mode. In adjoint mode,
CMFD acceleration is not currently supported and NEWT automatically
disables its use if*\ **cmfd=yes**\ *,*\ **=rect**\ *,
or*\ **=part**\ *. In adjoint mode with defined fixed source [i.e.,
generalized perturbation theory (GPT) analysis], it is observed that
tighter convergence and iteration parameters are needed to properly
remove fundamental mode contamination. (For more details, see SAMS
chapter: Generalized Perturbation Theory.) To facilitate the CMFD
options and larger convergence criteria for the forward calculations as
well as smaller convergence criteria for GPT adjoint calculations, the
following parameters are also available.h](hM)}(hXDefault convergence parameters are recommended for general analysis.
Larger convergence criteria are useful for debugging if shorter run time
is desired over solution accuracy. Smaller convergence criteria are
recommended for generating reference solutions or benchmark
calculations.h]h/XDefault convergence parameters are recommended for general analysis.
Larger convergence criteria are useful for debugging if shorter run time
is desired over solution accuracy. Smaller convergence criteria are
recommended for generating reference solutions or benchmark
calculations.}(hj)h j)ubah}(h]h]h]h]h]uhhLh!h"hMh j)ubhM)}(hX6CMFD acceleration should be applied whenever possible. The CMFD method
with second-level 2-group acceleration should be applied for
rectangular-domain configurations [e.g., light water reactor (LWR)
assembly models (*\ **cmfd=rect**\ *), by default*\ **cmfd2g=yes**\ *].
The unstructured CMFD method should be applied for triangular- or
hexagonal-domain configurations (*\ **cmfd=yes**\ *). If NEWT detects an
unstable CMFD condition, a warning message is printed and NEWT continues
with CMFD disabled. NEWT may also provide a terminating error message if
improper selection of the coarse mesh is detected. Internal
investigation has shown that the coarse mesh should be approximately the
same size as the unit cell used in the model. For LWR assembly models, a
fine mesh of 4 x 4 is recommended for the square-pitched unit cell,
implying that*\ **xycmfd**\ *should be 4 only if the global unit has a
mesh. If individual meshes are used in each unit definition, then the
global unit coarse-mesh cells should be sized based on the unit cell
size and, therefore, xycmfd=1 should be used. The values
of*\ **xcmfd**\ *and*\ **ycmfd**\ *do not have to be a common factor of
the number of fine-mesh cells in a given direction (NEWT will make the
last coarse-mesh cell smaller than the other coarse-mesh cells), but it
is highly recommended.h](h/CMFD acceleration should be applied whenever possible. The CMFD method
with second-level 2-group acceleration should be applied for
rectangular-domain configurations [e.g., light water reactor (LWR)
assembly models (}(hCMFD acceleration should be applied whenever possible. The CMFD method
with second-level 2-group acceleration should be applied for
rectangular-domain configurations [e.g., light water reactor (LWR)
assembly models (h j)ubj)}(h*\ **cmfd=rect**h]h/ **cmfd=rect*}(hhh j)ubah}(h]h]h]h]h]uhjh j)ubh/ }(h\ h j)ubj)}(h*), by default*h]h/
), by default}(hhh j)ubah}(h]h]h]h]h]uhjh j)ubh/ }(h\ h j)ubh)}(h**cmfd2g=yes**h]h/
cmfd2g=yes}(hhh j)ubah}(h]h]h]h]h]uhhh j)ubh/ }(h\ h j)ubj)}(hh*].
The unstructured CMFD method should be applied for triangular- or
hexagonal-domain configurations (*h]h/f].
The unstructured CMFD method should be applied for triangular- or
hexagonal-domain configurations (}(hhh j)ubah}(h]h]h]h]h]uhjh j)ubh/ }(h\ h j)ubh)}(h**cmfd=yes**h]h/cmfd=yes}(hhh j*ubah}(h]h]h]h]h]uhhh j)ubh/ }(h\ h j)ubj)}(hX*). If NEWT detects an
unstable CMFD condition, a warning message is printed and NEWT continues
with CMFD disabled. NEWT may also provide a terminating error message if
improper selection of the coarse mesh is detected. Internal
investigation has shown that the coarse mesh should be approximately the
same size as the unit cell used in the model. For LWR assembly models, a
fine mesh of 4 x 4 is recommended for the square-pitched unit cell,
implying that*h]h/X). If NEWT detects an
unstable CMFD condition, a warning message is printed and NEWT continues
with CMFD disabled. NEWT may also provide a terminating error message if
improper selection of the coarse mesh is detected. Internal
investigation has shown that the coarse mesh should be approximately the
same size as the unit cell used in the model. For LWR assembly models, a
fine mesh of 4 x 4 is recommended for the square-pitched unit cell,
implying that}(hhh j*ubah}(h]h]h]h]h]uhjh j)ubh/ }(h\ h j)ubh)}(h
**xycmfd**h]h/xycmfd}(hhh j.*ubah}(h]h]h]h]h]uhhh j)ubh/ }(h\ h j)ubj)}(h*should be 4 only if the global unit has a
mesh. If individual meshes are used in each unit definition, then the
global unit coarse-mesh cells should be sized based on the unit cell
size and, therefore, xycmfd=1 should be used. The values
of*h]h/should be 4 only if the global unit has a
mesh. If individual meshes are used in each unit definition, then the
global unit coarse-mesh cells should be sized based on the unit cell
size and, therefore, xycmfd=1 should be used. The values
of}(hhh jA*ubah}(h]h]h]h]h]uhjh j)ubh/ }(h\ h j)ubh)}(h **xcmfd**h]h/xcmfd}(hhh jT*ubah}(h]h]h]h]h]uhhh j)ubh/ }(h\ h j)ubj)}(h*and*h]h/and}(hhh jg*ubah}(h]h]h]h]h]uhjh j)ubh/ }(h\ h j)ubh)}(h **ycmfd**h]h/ycmfd}(hhh jz*ubah}(h]h]h]h]h]uhhh j)ubh/ }(hj)h j)ubh problematic)}(hj,h]h/*}(hhh j*ubah}(h]id44ah]h]h]h]refidid43uhj*h j)ubh/do not have to be a common factor of
the number of fine-mesh cells in a given direction (NEWT will make the
last coarse-mesh cell smaller than the other coarse-mesh cells), but it
is highly recommended.}(hdo not have to be a common factor of
the number of fine-mesh cells in a given direction (NEWT will make the
last coarse-mesh cell smaller than the other coarse-mesh cells), but it
is highly recommended.h j)ubeh}(h]h]h]h]h]uhhLh!h"hMh j)ubhM)}(hXUsers can gauge solution convergence by the outer iteration edit as it
is printed to the terminal window (*\ **echo=yes**\ *, see below). One
can terminate a calculation prematurely (via the Control-C option on
most platforms) if convergence or iteration parameters need to be
modified.h](h/jUsers can gauge solution convergence by the outer iteration edit as it
is printed to the terminal window (}(hjUsers can gauge solution convergence by the outer iteration edit as it
is printed to the terminal window (h j*ubj)}(h*\ **echo=yes**h]h/
**echo=yes*}(hhh j*ubah}(h]h]h]h]h]uhjh j*ubh/ }(h\ h j*ubj*)}(hj,h]h/*}(hhh j*ubah}(h]id46ah]h]h]h]refidid45uhj*h j*ubh/, see below). One
can terminate a calculation prematurely (via the Control-C option on
most platforms) if convergence or iteration parameters need to be
modified.}(h, see below). One
can terminate a calculation prematurely (via the Control-C option on
most platforms) if convergence or iteration parameters need to be
modified.h j*ubeh}(h]h]h]h]h]uhhLh!h"hMh j)ubhM)}(hXThe TRITON control module supports a sensitivity and uncertainty
analysis sequence TSUNAMI-2D (See TRITON chapter, section S/U Analysis
Sequences (TSUNAMI-2D, TSUNAMI-2DC)). TSUNAMI-2D calculations require
NEWT to be run in both forward mode and adjoint mode. In adjoint mode,
CMFD acceleration is not currently supported and NEWT automatically
disables its use if*\ **cmfd=yes**\ *,*\ **=rect**\ *,
or*\ **=part**\ *. In adjoint mode with defined fixed source [i.e.,
generalized perturbation theory (GPT) analysis], it is observed that
tighter convergence and iteration parameters are needed to properly
remove fundamental mode contamination. (For more details, see SAMS
chapter: Generalized Perturbation Theory.) To facilitate the CMFD
options and larger convergence criteria for the forward calculations as
well as smaller convergence criteria for GPT adjoint calculations, the
following parameters are also available.h](h/XoThe TRITON control module supports a sensitivity and uncertainty
analysis sequence TSUNAMI-2D (See TRITON chapter, section S/U Analysis
Sequences (TSUNAMI-2D, TSUNAMI-2DC)). TSUNAMI-2D calculations require
NEWT to be run in both forward mode and adjoint mode. In adjoint mode,
CMFD acceleration is not currently supported and NEWT automatically
disables its use if* }(hXoThe TRITON control module supports a sensitivity and uncertainty
analysis sequence TSUNAMI-2D (See TRITON chapter, section S/U Analysis
Sequences (TSUNAMI-2D, TSUNAMI-2DC)). TSUNAMI-2D calculations require
NEWT to be run in both forward mode and adjoint mode. In adjoint mode,
CMFD acceleration is not currently supported and NEWT automatically
disables its use if*\ h j*ubh)}(h**cmfd=yes**h]h/cmfd=yes}(hhh j*ubah}(h]h]h]h]h]uhhh j*ubh/ }(h\ h j*ubj)}(h*,*h]h/,}(hhh j*ubah}(h]h]h]h]h]uhjh j*ubh/ }(h\ h j*ubh)}(h **=rect**h]h/=rect}(hhh j+ubah}(h]h]h]h]h]uhhh j*ubh/ }(h\ h j*ubj)}(h*,
or*h]h/,
or}(hhh j"+ubah}(h]h]h]h]h]uhjh j*ubh/ }(h\ h j*ubh)}(h **=part**h]h/=part}(hhh j5+ubah}(h]h]h]h]h]uhhh j*ubh/ }(hj*h j*ubj*)}(hj,h]h/*}(hhh jG+ubah}(h]id48ah]h]h]h]refidid47uhj*h j*ubh/X. In adjoint mode with defined fixed source [i.e.,
generalized perturbation theory (GPT) analysis], it is observed that
tighter convergence and iteration parameters are needed to properly
remove fundamental mode contamination. (For more details, see SAMS
chapter: Generalized Perturbation Theory.) To facilitate the CMFD
options and larger convergence criteria for the forward calculations as
well as smaller convergence criteria for GPT adjoint calculations, the
following parameters are also available.}(hX. In adjoint mode with defined fixed source [i.e.,
generalized perturbation theory (GPT) analysis], it is observed that
tighter convergence and iteration parameters are needed to properly
remove fundamental mode contamination. (For more details, see SAMS
chapter: Generalized Perturbation Theory.) To facilitate the CMFD
options and larger convergence criteria for the forward calculations as
well as smaller convergence criteria for GPT adjoint calculations, the
following parameters are also available.h j*ubeh}(h]h]h]h]h]uhhLh!h"hMh j)ubeh}(h]h]h]h]h]uhj)h j%hhh!h"hNubhM)}(hi**gptepsinner=**\ (*RN*) — Spatial convergence criterion for inner
iterations in GPT analysis. [0.0001]h](h)}(h**gptepsinner=**h]h/gptepsinner=}(hhh jl+ubah}(h]h]h]h]h]uhhh jh+ubh/ (}(h\ (h jh+hhh!NhNubj)}(h*RN*h]h/RN}(hhh j+ubah}(h]h]h]h]h]uhjh jh+ubh/R) — Spatial convergence criterion for inner
iterations in GPT analysis. [0.0001]}(hR) — Spatial convergence criterion for inner
iterations in GPT analysis. [0.0001]h jh+hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j%hhubhM)}(hh**gptepsouter=**\ (*RN*) — Spatial convergence criterion for outer
iterations in GPT analysis. [0.001]h](h)}(h**gptepsouter=**h]h/gptepsouter=}(hhh j+ubah}(h]h]h]h]h]uhhh j+ubh/ (}(h\ (h j+hhh!NhNubj)}(h*RN*h]h/RN}(hhh j+ubah}(h]h]h]h]h]uhjh j+ubh/Q) — Spatial convergence criterion for outer
iterations in GPT analysis. [0.001]}(hQ) — Spatial convergence criterion for outer
iterations in GPT analysis. [0.001]h j+hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j%hhubhM)}(h**gptepsthrm=**\ (*RN*) — Spatial convergence criterion for
thermal-upscattering iterations, if enabled, in GPT analysis. [same
value as **gptepsouter**]h](h)}(h**gptepsthrm=**h]h/gptepsthrm=}(hhh j+ubah}(h]h]h]h]h]uhhh j+ubh/ (}(h\ (h j+hhh!NhNubj)}(h*RN*h]h/RN}(hhh j+ubah}(h]h]h]h]h]uhjh j+ubh/u) — Spatial convergence criterion for
thermal-upscattering iterations, if enabled, in GPT analysis. [same
value as }(hu) — Spatial convergence criterion for
thermal-upscattering iterations, if enabled, in GPT analysis. [same
value as h j+hhh!NhNubh)}(h**gptepsouter**h]h/gptepsouter}(hhh j+ubah}(h]h]h]h]h]uhhh j+ubh/]}(hj"&h j+hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j%hhubhM)}(h**gptsepsilon=**\ (*RN*) — Simultaneously sets all spatial convergence
criteria to the same value in GPT analysis. [uses individual defaults]h](h)}(h**gptsepsilon=**h]h/gptsepsilon=}(hhh j,ubah}(h]h]h]h]h]uhhh j
,ubh/ (}(h\ (h j
,hhh!NhNubj)}(h*RN*h]h/RN}(hhh j!,ubah}(h]h]h]h]h]uhjh j
,ubh/x) — Simultaneously sets all spatial convergence
criteria to the same value in GPT analysis. [uses individual defaults]}(hx) — Simultaneously sets all spatial convergence
criteria to the same value in GPT analysis. [uses individual defaults]h j
,hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j%hhubhM)}(hg**gpttherm**\ =(\ *yes/no*) — Enables/disables thermal-upscattering
iterations in GPT analysis. [yes]h](h)}(h**gpttherm**h]h/gpttherm}(hhh j>,ubah}(h]h]h]h]h]uhhh j:,ubh/ =( }(h\ =(\ h j:,hhh!NhNubj)}(h*yes/no*h]h/yes/no}(hhh jQ,ubah}(h]h]h]h]h]uhjh j:,ubh/M) — Enables/disables thermal-upscattering
iterations in GPT analysis. [yes]}(hM) — Enables/disables thermal-upscattering
iterations in GPT analysis. [yes]h j:,hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j%hhubhM)}(hg**gptinners=**\ (*IN*) — Maximum number of inner iterations in an energy
group in GPT analysis. [500]h](h)}(h**gptinners=**h]h/
gptinners=}(hhh jn,ubah}(h]h]h]h]h]uhhh jj,ubh/ (}(h\ (h jj,hhh!NhNubj)}(h*IN*h]h/IN}(hhh j,ubah}(h]h]h]h]h]uhjh jj,ubh/R) — Maximum number of inner iterations in an energy
group in GPT analysis. [500]}(hR) — Maximum number of inner iterations in an energy
group in GPT analysis. [500]h jj,hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j%hhubhM)}(ho**gpttherms=**\ (*IN*) — Maximum number of thermal-upscattering
iterations, if enabled, in GPT analysis. [10]h](h)}(h**gpttherms=**h]h/
gpttherms=}(hhh j,ubah}(h]h]h]h]h]uhhh j,ubh/ (}(h\ (h j,hhh!NhNubj)}(h*IN*h]h/IN}(hhh j,ubah}(h]h]h]h]h]uhjh j,ubh/Z) — Maximum number of thermal-upscattering
iterations, if enabled, in GPT analysis. [10]}(hZ) — Maximum number of thermal-upscattering
iterations, if enabled, in GPT analysis. [10]h j,hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j%hhubhM)}(h**gptouters=**\ (*IN*) — Maximum number of outer iterations in GPT
analysis. NEWT will stop with an error code if more than *outers* outer
iterations are required for convergence. [2000]h](h)}(h**gptouters=**h]h/
gptouters=}(hhh j,ubah}(h]h]h]h]h]uhhh j,ubh/ (}(h\ (h j,hhh!NhNubj)}(h*IN*h]h/IN}(hhh j,ubah}(h]h]h]h]h]uhjh j,ubh/i) — Maximum number of outer iterations in GPT
analysis. NEWT will stop with an error code if more than }(hi) — Maximum number of outer iterations in GPT
analysis. NEWT will stop with an error code if more than h j,hhh!NhNubj)}(h*outers*h]h/outers}(hhh j,ubah}(h]h]h]h]h]uhjh j,ubh/6 outer
iterations are required for convergence. [2000]}(h6 outer
iterations are required for convergence. [2000]h j,hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j%hhubj))}(hXDefault values for GPT convergence may change with future releases, as
more experience is gained and user feedback is received. If the GPT
calculation is not converging because of fundamental mode contamination,
it is recommended that convergence criteria be decreased and/or inner
and thermal-upscattering iteration limits be increased. If the solution
convergence is slow,*\ **gptinners**\ *can potentially be decreased.
Again, it is highly recommended that*\ **echo=yes**\ *be used to monitor
speed of convergence.h]hM)}(hXDefault values for GPT convergence may change with future releases, as
more experience is gained and user feedback is received. If the GPT
calculation is not converging because of fundamental mode contamination,
it is recommended that convergence criteria be decreased and/or inner
and thermal-upscattering iteration limits be increased. If the solution
convergence is slow,*\ **gptinners**\ *can potentially be decreased.
Again, it is highly recommended that*\ **echo=yes**\ *be used to monitor
speed of convergence.h](h/XyDefault values for GPT convergence may change with future releases, as
more experience is gained and user feedback is received. If the GPT
calculation is not converging because of fundamental mode contamination,
it is recommended that convergence criteria be decreased and/or inner
and thermal-upscattering iteration limits be increased. If the solution
convergence is slow,* }(hXyDefault values for GPT convergence may change with future releases, as
more experience is gained and user feedback is received. If the GPT
calculation is not converging because of fundamental mode contamination,
it is recommended that convergence criteria be decreased and/or inner
and thermal-upscattering iteration limits be increased. If the solution
convergence is slow,*\ h j-ubh)}(h
**gptinners**h]h/ gptinners}(hhh j-ubah}(h]h]h]h]h]uhhh j-ubh/ }(h\ h j-ubj)}(hD*can potentially be decreased.
Again, it is highly recommended that*h]h/Bcan potentially be decreased.
Again, it is highly recommended that}(hhh j--ubah}(h]h]h]h]h]uhjh j-ubh/ }(h\ h j-ubh)}(h**echo=yes**h]h/echo=yes}(hhh j@-ubah}(h]h]h]h]h]uhhh j-ubh/ }(hj,-h j-ubj*)}(hj,h]h/*}(hhh jR-ubah}(h]id50ah]h]h]h]refidid49uhj*h j-ubh/(be used to monitor
speed of convergence.}(h(be used to monitor
speed of convergence.h j-ubeh}(h]h]h]h]h]uhhLh!h"hMh j
-ubah}(h]h]h]h]h]uhj)h j%hhh!h"hNubh)}(h.. _9-2-3-2-2:h]h}(h]h]h]h]h]hid51uhh
hMh j%hhh!h"ubeh}(h]('convergence-and-acceleration-parametersj%eh]h]('convergence and acceleration parameters 9-2-3-2-1eh]h]uhh#h j$hhh!h"hMMj}j-j%sj}j%j%subh$)}(hhh](h))}(hOutput editingh]h/Output editing}(hj-h j-hhh!NhNubah}(h]h]h]h]h]uhh(h j-hhh!h"hMubhM)}(hX6**drawit=**\ (*yes/no*) — Create a PostScript file showing the grid
structure determined from input. Two files are created—the first showing
the grid structure and the second showing the material placement.
(Features and use of this simple graphics capability are described
further in :ref:`9-2-5-14`) [no]h](h)}(h**drawit=**h]h/drawit=}(hhh j-ubah}(h]h]h]h]h]uhhh j-ubh/ (}(h\ (h j-hhh!NhNubj)}(h*yes/no*h]h/yes/no}(hhh j-ubah}(h]h]h]h]h]uhjh j-ubh/X) — Create a PostScript file showing the grid
structure determined from input. Two files are created—the first showing
the grid structure and the second showing the material placement.
(Features and use of this simple graphics capability are described
further in }(hX) — Create a PostScript file showing the grid
structure determined from input. Two files are created—the first showing
the grid structure and the second showing the material placement.
(Features and use of this simple graphics capability are described
further in h j-hhh!NhNubj)}(h:ref:`9-2-5-14`h]j)}(hj-h]h/9-2-5-14}(hhh j-ubah}(h]h](jEstdstd-refeh]h]h]uhjh j-ubah}(h]h]h]h]h]refdochj refdomainj-reftyperefrefexplicitrefwarnjW9-2-5-14uhjh!h"hMh j-ubh/) [no]}(h) [no]h j-hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j-hhubhM)}(h**echo=**\ (*yes/no*) — During the iteration phase of execution, output
is generated at the beginning of each outer iteration. This same
information can be printed to SCALE message file (.msg) during iteration
by setting echo=yes. [no]h](h)}(h **echo=**h]h/echo=}(hhh j-ubah}(h]h]h]h]h]uhhh j-ubh/ (}(h\ (h j-hhh!NhNubj)}(h*yes/no*h]h/yes/no}(hhh j.ubah}(h]h]h]h]h]uhjh j-ubh/) — During the iteration phase of execution, output
is generated at the beginning of each outer iteration. This same
information can be printed to SCALE message file (.msg) during iteration
by setting echo=yes. [no]}(h) — During the iteration phase of execution, output
is generated at the beginning of each outer iteration. This same
information can be printed to SCALE message file (.msg) during iteration
by setting echo=yes. [no]h j-hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j-hhubhM)}(h}**prtbalnc**\ =\ *(yes/no)* — Flag indicating whether or not balance
tables for fine-group mixtures should be printed. [no]h](h)}(h**prtbalnc**h]h/prtbalnc}(hhh j#.ubah}(h]h]h]h]h]uhhh j.ubh/ = }(h\ =\ h j.hhh!NhNubj)}(h
*(yes/no)*h]h/(yes/no)}(hhh j6.ubah}(h]h]h]h]h]uhjh j.ubh/b — Flag indicating whether or not balance
tables for fine-group mixtures should be printed. [no]}(hb — Flag indicating whether or not balance
tables for fine-group mixtures should be printed. [no]h j.hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j-hhubhM)}(hX**prtbroad=**\ (*yes/no/1d*) — Flag indicating whether or not broad
group cross sections should be printed in problem output. The *1d*
option indicates that 2-D scattering tables are not to be printed. This
flag has no effect if collapse=no is specified. [no]h](h)}(h
**prtbroad=**h]h/ prtbroad=}(hhh jS.ubah}(h]h]h]h]h]uhhh jO.ubh/ (}(h\ (h jO.hhh!NhNubj)}(h*yes/no/1d*h]h/ yes/no/1d}(hhh jf.ubah}(h]h]h]h]h]uhjh jO.ubh/j) — Flag indicating whether or not broad
group cross sections should be printed in problem output. The }(hj) — Flag indicating whether or not broad
group cross sections should be printed in problem output. The h jO.hhh!NhNubj)}(h*1d*h]h/1d}(hhh jy.ubah}(h]h]h]h]h]uhjh jO.ubh/}
option indicates that 2-D scattering tables are not to be printed. This
flag has no effect if collapse=no is specified. [no]}(h}
option indicates that 2-D scattering tables are not to be printed. This
flag has no effect if collapse=no is specified. [no]h jO.hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j-hhubhM)}(h**prthmmix=**\ (*yes/no*) — Flag indicating whether or not homogenized
mixture macroscopic cross sections should be printed in problem output.
Homogenized cross sections are printed only if Homogenization Block is
provided (:ref:`9-2-3-10`). [yes]h](h)}(h
**prthmmix=**h]h/ prthmmix=}(hhh j.ubah}(h]h]h]h]h]uhhh j.ubh/ (}(h\ (h j.hhh!NhNubj)}(h*yes/no*h]h/yes/no}(hhh j.ubah}(h]h]h]h]h]uhjh j.ubh/) — Flag indicating whether or not homogenized
mixture macroscopic cross sections should be printed in problem output.
Homogenized cross sections are printed only if Homogenization Block is
provided (}(h) — Flag indicating whether or not homogenized
mixture macroscopic cross sections should be printed in problem output.
Homogenized cross sections are printed only if Homogenization Block is
provided (h j.hhh!NhNubj)}(h:ref:`9-2-3-10`h]j)}(hj.h]h/9-2-3-10}(hhh j.ubah}(h]h](jEstdstd-refeh]h]h]uhjh j.ubah}(h]h]h]h]h]refdochj refdomainj.reftyperefrefexplicitrefwarnjW9-2-3-10uhjh!h"hMh j.ubh/). [yes]}(h). [yes]h j.hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j-hhubhM)}(h**prtflux**\ *=(yes/no)* — Create a PostScript plot file showing flux
distribution for each energy group in problem. If an energy collapse is
performed, a second plot file is generated for the fluxes of the
collapsed group structures. [no]h](h)}(h**prtflux**h]h/prtflux}(hhh j.ubah}(h]h]h]h]h]uhhh j.ubh/ }(h\ h j.hhh!NhNubj)}(h*=(yes/no)*h]h/ =(yes/no)}(hhh j.ubah}(h]h]h]h]h]uhjh j.ubh/ — Create a PostScript plot file showing flux
distribution for each energy group in problem. If an energy collapse is
performed, a second plot file is generated for the fluxes of the
collapsed group structures. [no]}(h — Create a PostScript plot file showing flux
distribution for each energy group in problem. If an energy collapse is
performed, a second plot file is generated for the fluxes of the
collapsed group structures. [no]h j.hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j-hhubhM)}(h**prtmxsec=**\ (*yes/no/1d*) — Flag indicating whether or not mixture
macroscopic cross sections should be printed in problem output. The *1d*
option indicates that 2-D scattering tables are not to be printed. [no]h](h)}(h
**prtmxsec=**h]h/ prtmxsec=}(hhh j/ubah}(h]h]h]h]h]uhhh j/ubh/ (}(h\ (h j/hhh!NhNubj)}(h*yes/no/1d*h]h/ yes/no/1d}(hhh j./ubah}(h]h]h]h]h]uhjh j/ubh/r) — Flag indicating whether or not mixture
macroscopic cross sections should be printed in problem output. The }(hr) — Flag indicating whether or not mixture
macroscopic cross sections should be printed in problem output. The h j/hhh!NhNubj)}(h*1d*h]h/1d}(hhh jA/ubah}(h]h]h]h]h]uhjh j/ubh/H
option indicates that 2-D scattering tables are not to be printed. [no]}(hH
option indicates that 2-D scattering tables are not to be printed. [no]h j/hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j-hhubhM)}(h}**prtmxtab=**\ (*yes/no*) — Flag indicating whether or not the input
mixing table should be printed in problem output. [no]h](h)}(h
**prtmxtab=**h]h/ prtmxtab=}(hhh j^/ubah}(h]h]h]h]h]uhhh jZ/ubh/ (}(h\ (h jZ/hhh!NhNubj)}(h*yes/no*h]h/yes/no}(hhh jq/ubah}(h]h]h]h]h]uhjh jZ/ubh/e) — Flag indicating whether or not the input
mixing table should be printed in problem output. [no]}(he) — Flag indicating whether or not the input
mixing table should be printed in problem output. [no]h jZ/hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j-hhubhM)}(h**prtxsec=**\ (*yes/no/1d*) — Flag indicating whether or not input
microscopic cross sections should be printed in problem output. The *1d*
option indicates that 2-D scattering tables are not to be printed. [no]h](h)}(h**prtxsec=**h]h/prtxsec=}(hhh j/ubah}(h]h]h]h]h]uhhh j/ubh/ (}(h\ (h j/hhh!NhNubj)}(h*yes/no/1d*h]h/ yes/no/1d}(hhh j/ubah}(h]h]h]h]h]uhjh j/ubh/p) — Flag indicating whether or not input
microscopic cross sections should be printed in problem output. The }(hp) — Flag indicating whether or not input
microscopic cross sections should be printed in problem output. The h j/hhh!NhNubj)}(h*1d*h]h/1d}(hhh j/ubah}(h]h]h]h]h]uhjh j/ubh/H
option indicates that 2-D scattering tables are not to be printed. [no]}(hH
option indicates that 2-D scattering tables are not to be printed. [no]h j/hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j-hhubhM)}(hU**timed=**\ (yes/no) — Turns on printing of iteration timing and CPU use
data. [no]h](h)}(h
**timed=**h]h/timed=}(hhh j/ubah}(h]h]h]h]h]uhhh j/ubh/K (yes/no) — Turns on printing of iteration timing and CPU use
data. [no]}(hK\ (yes/no) — Turns on printing of iteration timing and CPU use
data. [no]h j/hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j-hhubhM)}(hX'**det=**\ (*IN*) — Specifies the mixture used to represent a local power
range monitor (LPRM) and/or Traversing In-core Probe (TIP) detector
located within a fuel lattice. The mixture must also be included in a
homogenization block in order to obtain detector cross sections. [has no
default]h](h)}(h**det=**h]h/det=}(hhh j/ubah}(h]h]h]h]h]uhhh j/ubh/ (}(h\ (h j/hhh!NhNubj)}(h*IN*h]h/IN}(hhh j0ubah}(h]h]h]h]h]uhjh j/ubh/X) — Specifies the mixture used to represent a local power
range monitor (LPRM) and/or Traversing In-core Probe (TIP) detector
located within a fuel lattice. The mixture must also be included in a
homogenization block in order to obtain detector cross sections. [has no
default]}(hX) — Specifies the mixture used to represent a local power
range monitor (LPRM) and/or Traversing In-core Probe (TIP) detector
located within a fuel lattice. The mixture must also be included in a
homogenization block in order to obtain detector cross sections. [has no
default]h j/hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j-hhubj))}(hXWith the exception of*\ **prthmmix**\ *, all output edit options are
disabled unless requested by the user. The output edits are disabled by
default to minimize the size of the output. The*\ **drawit**\ *option is
recommended to generate PostScript plots of the model grid structure and
material placement. As previously mentioned,
the*\ **echo**\ *and*\ **timed**\ *options are recommended to monitor
solution convergence. If the timed option is enabled, each line in the
outer iteration edit will be longer than 80 characters. Therefore, it is
recommended that Windows users should increase the Command Window size
from 80 characters to 132* characters.h]hM)}(hXWith the exception of*\ **prthmmix**\ *, all output edit options are
disabled unless requested by the user. The output edits are disabled by
default to minimize the size of the output. The*\ **drawit**\ *option is
recommended to generate PostScript plots of the model grid structure and
material placement. As previously mentioned,
the*\ **echo**\ *and*\ **timed**\ *options are recommended to monitor
solution convergence. If the timed option is enabled, each line in the
outer iteration edit will be longer than 80 characters. Therefore, it is
recommended that Windows users should increase the Command Window size
from 80 characters to 132* characters.h](h/With the exception of* }(hWith the exception of*\ h j0ubh)}(h**prthmmix**h]h/prthmmix}(hhh j'0ubah}(h]h]h]h]h]uhhh j0ubh/ }(h\ h j0ubj)}(h*, all output edit options are
disabled unless requested by the user. The output edits are disabled by
default to minimize the size of the output. The*h]h/, all output edit options are
disabled unless requested by the user. The output edits are disabled by
default to minimize the size of the output. The}(hhh j:0ubah}(h]h]h]h]h]uhjh j0ubh/ }(h\ h j0ubh)}(h
**drawit**h]h/drawit}(hhh jM0ubah}(h]h]h]h]h]uhhh j0ubh/ }(h\ h j0ubj)}(h*option is
recommended to generate PostScript plots of the model grid structure and
material placement. As previously mentioned,
the*h]h/option is
recommended to generate PostScript plots of the model grid structure and
material placement. As previously mentioned,
the}(hhh j`0ubah}(h]h]h]h]h]uhjh j0ubh/ }(h\ h j0ubh)}(h**echo**h]h/echo}(hhh js0ubah}(h]h]h]h]h]uhhh j0ubh/ }(h\ h j0ubj)}(h*and*h]h/and}(hhh j0ubah}(h]h]h]h]h]uhjh j0ubh/ }(h\ h j0ubh)}(h **timed**h]h/timed}(hhh j0ubah}(h]h]h]h]h]uhhh j0ubh/ }(hj90h j0ubj)}(hX*options are recommended to monitor
solution convergence. If the timed option is enabled, each line in the
outer iteration edit will be longer than 80 characters. Therefore, it is
recommended that Windows users should increase the Command Window size
from 80 characters to 132*h]h/Xoptions are recommended to monitor
solution convergence. If the timed option is enabled, each line in the
outer iteration edit will be longer than 80 characters. Therefore, it is
recommended that Windows users should increase the Command Window size
from 80 characters to 132}(hhh j0ubah}(h]h]h]h]h]uhjh j0ubh/
characters.}(h
characters.h j0ubeh}(h]h]h]h]h]uhhLh!h"hM h j0ubah}(h]h]h]h]h]uhj)h j-hhh!h"hNubh)}(h.. _9-2-3-2-3:h]h}(h]h]h]h]h]hid52uhh
hM+h j-hhh!h"ubeh}(h](output-editingj}-eh]h](output editing 9-2-3-2-2eh]h]uhh#h j$hhh!h"hMj}j0js-sj}j}-js-subh$)}(hhh](h))}(hAngular quadratureh]h/Angular quadrature}(hj0h j0hhh!NhNubah}(h]h]h]h]h]uhh(h j0hhh!h"hM.ubhM)}(hT**sn=**\ (*2/4/6/8/10/12/14/16*) — Order of Sn level symmetric
quadrature set. [6]h](h)}(h**sn=**h]h/sn=}(hhh j0ubah}(h]h]h]h]h]uhhh j0ubh/ (}(h\ (h j0hhh!NhNubj)}(h*2/4/6/8/10/12/14/16*h]h/2/4/6/8/10/12/14/16}(hhh j1ubah}(h]h]h]h]h]uhjh j0ubh/5) — Order of Sn level symmetric
quadrature set. [6]}(h5) — Order of Sn level symmetric
quadrature set. [6]h j0hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM0h j0hhubhM)}(hXK**nazim**\ =(\ *IN*) — Number of equally spaced azimuthal directions in
a product quadrature set. Used in tandem with *npolar* keyword (both
must be specified). Total number of angles in the product quadrature set
is the product of *nazim* and *npolar*. [No default. If not specified,
level symmetric quadrature default is used.]h](h)}(h **nazim**h]h/nazim}(hhh j%1ubah}(h]h]h]h]h]uhhh j!1ubh/ =( }(h\ =(\ h j!1hhh!NhNubj)}(h*IN*h]h/IN}(hhh j81ubah}(h]h]h]h]h]uhjh j!1ubh/e) — Number of equally spaced azimuthal directions in
a product quadrature set. Used in tandem with }(he) — Number of equally spaced azimuthal directions in
a product quadrature set. Used in tandem with h j!1hhh!NhNubj)}(h*npolar*h]h/npolar}(hhh jK1ubah}(h]h]h]h]h]uhjh j!1ubh/j keyword (both
must be specified). Total number of angles in the product quadrature set
is the product of }(hj keyword (both
must be specified). Total number of angles in the product quadrature set
is the product of h j!1hhh!NhNubj)}(h*nazim*h]h/nazim}(hhh j^1ubah}(h]h]h]h]h]uhjh j!1ubh/ and }(h and h j!1hhh!NhNubj)}(h*npolar*h]h/npolar}(hhh jq1ubah}(h]h]h]h]h]uhjh j!1ubh/M. [No default. If not specified,
level symmetric quadrature default is used.]}(hM. [No default. If not specified,
level symmetric quadrature default is used.]h j!1hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM3h j0hhubhM)}(hXc**npolar**\ =(\ *IN*) — Number of polar angles in a product quadrature
set (determined using a Gauss-Legendre polynomial). Used in tandem with
*nazim* keyword (both must be specified). Total number of angles in the
product quadrature set is the product of *nazim* and *npolar*. [No
default. If not specified, level symmetric quadrature default is used.]h](h)}(h
**npolar**h]h/npolar}(hhh j1ubah}(h]h]h]h]h]uhhh j1ubh/ =( }(h\ =(\ h j1hhh!NhNubj)}(h*IN*h]h/IN}(hhh j1ubah}(h]h]h]h]h]uhjh j1ubh/}) — Number of polar angles in a product quadrature
set (determined using a Gauss-Legendre polynomial). Used in tandem with
}(h}) — Number of polar angles in a product quadrature
set (determined using a Gauss-Legendre polynomial). Used in tandem with
h j1hhh!NhNubj)}(h*nazim*h]h/nazim}(hhh j1ubah}(h]h]h]h]h]uhjh j1ubh/j keyword (both must be specified). Total number of angles in the
product quadrature set is the product of }(hj keyword (both must be specified). Total number of angles in the
product quadrature set is the product of h j1hhh!NhNubj)}(h*nazim*h]h/nazim}(hhh j1ubah}(h]h]h]h]h]uhjh j1ubh/ and }(h and h j1hhh!NhNubj)}(h*npolar*h]h/npolar}(hhh j1ubah}(h]h]h]h]h]uhjh j1ubh/M. [No
default. If not specified, level symmetric quadrature default is used.]}(hM. [No
default. If not specified, level symmetric quadrature default is used.]h j1hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM9h j0hhubhM)}(h**dgauss=**\ (yes/no) — Enables/disables use of double Gauss-Legendre
product quadrature set. If disabled, single Gauss-Legendre product
quadrature sets are used. [no]h](h)}(h**dgauss=**h]h/dgauss=}(hhh j1ubah}(h]h]h]h]h]uhhh j1ubh/ (yes/no) — Enables/disables use of double Gauss-Legendre
product quadrature set. If disabled, single Gauss-Legendre product
quadrature sets are used. [no]}(h\ (yes/no) — Enables/disables use of double Gauss-Legendre
product quadrature set. If disabled, single Gauss-Legendre product
quadrature sets are used. [no]h j1hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM?h j0hhubj))}(hXIf both level symmetric quadrature sets and product quadrature sets are
requested, the level symmetric quadrature set is to be used. Level
symmetric quadrature sets are recommended for general analysis. If
reflective boundary conditions are desired for hexagonal-domain
configurations, product quadrature sets must be used and nazim must be a
multiple of 3. If reflective boundary conditions are desired for
triangular-domain configurations, product quadrature sets must be used
and*\ **nazim**\ *must be an odd number.h]hM)}(hXIf both level symmetric quadrature sets and product quadrature sets are
requested, the level symmetric quadrature set is to be used. Level
symmetric quadrature sets are recommended for general analysis. If
reflective boundary conditions are desired for hexagonal-domain
configurations, product quadrature sets must be used and nazim must be a
multiple of 3. If reflective boundary conditions are desired for
triangular-domain configurations, product quadrature sets must be used
and*\ **nazim**\ *must be an odd number.h](h/XIf both level symmetric quadrature sets and product quadrature sets are
requested, the level symmetric quadrature set is to be used. Level
symmetric quadrature sets are recommended for general analysis. If
reflective boundary conditions are desired for hexagonal-domain
configurations, product quadrature sets must be used and nazim must be a
multiple of 3. If reflective boundary conditions are desired for
triangular-domain configurations, product quadrature sets must be used
and* }(hXIf both level symmetric quadrature sets and product quadrature sets are
requested, the level symmetric quadrature set is to be used. Level
symmetric quadrature sets are recommended for general analysis. If
reflective boundary conditions are desired for hexagonal-domain
configurations, product quadrature sets must be used and nazim must be a
multiple of 3. If reflective boundary conditions are desired for
triangular-domain configurations, product quadrature sets must be used
and*\ h j2ubh)}(h **nazim**h]h/nazim}(hhh j2ubah}(h]h]h]h]h]uhhh j2ubh/ }(h\ h j2ubj*)}(hj,h]h/*}(hhh j02ubah}(h]id54ah]h]h]h]refidid53uhj*h j2ubh/must be an odd number.}(hmust be an odd number.h j2ubeh}(h]h]h]h]h]uhhLh!h"hMCh j2ubah}(h]h]h]h]h]uhj)h j0hhh!h"hNubh)}(h.. _9-2-3-2-4:h]h}(h]h]h]h]h]hid55uhh
hMLh j0hhh!h"ubeh}(h](angular-quadraturej0eh]h](angular quadrature 9-2-3-2-3eh]h]uhh#h j$hhh!h"hM.j}jb2j0sj}j0j0subh$)}(hhh](h))}(hControl optionsh]h/Control options}(hjl2h jj2hhh!NhNubah}(h]h]h]h]h]uhh(h jg2hhh!h"hMOubhM)}(h|**adjoint=**\ (*yes/no*) — This keyword specifies either a forward
(adjoint=no) or adjoint (adjoint=yes) calculation. [no]h](h)}(h**adjoint=**h]h/adjoint=}(hhh j|2ubah}(h]h]h]h]h]uhhh jx2ubh/ (}(h\ (h jx2hhh!NhNubj)}(h*yes/no*h]h/yes/no}(hhh j2ubah}(h]h]h]h]h]uhjh jx2ubh/e) — This keyword specifies either a forward
(adjoint=no) or adjoint (adjoint=yes) calculation. [no]}(he) — This keyword specifies either a forward
(adjoint=no) or adjoint (adjoint=yes) calculation. [no]h jx2hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMQh jg2hhubhM)}(h**forward=**\ (*yes/no*) — This keyword specifies either a forward
(forward=yes) or adjoint (forward=no) calculation. If adjoint and
forward are both specified, NEWT uses the last specification. [yes]h](h)}(h**forward=**h]h/forward=}(hhh j2ubah}(h]h]h]h]h]uhhh j2ubh/ (}(h\ (h j2hhh!NhNubj)}(h*yes/no*h]h/yes/no}(hhh j2ubah}(h]h]h]h]h]uhjh j2ubh/) — This keyword specifies either a forward
(forward=yes) or adjoint (forward=no) calculation. If adjoint and
forward are both specified, NEWT uses the last specification. [yes]}(h) — This keyword specifies either a forward
(forward=yes) or adjoint (forward=no) calculation. If adjoint and
forward are both specified, NEWT uses the last specification. [yes]h j2hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMTh jg2hhubhM)}(h**gpt=**\ (*yes/no*) — This keyword specifies whether this is a GPT
adjoint calculation. The *gpt* keyword is active only for adjoint
calculations. [no]h](h)}(h**gpt=**h]h/gpt=}(hhh j2ubah}(h]h]h]h]h]uhhh j2ubh/ (}(h\ (h j2hhh!NhNubj)}(h*yes/no*h]h/yes/no}(hhh j2ubah}(h]h]h]h]h]uhjh j2ubh/L) — This keyword specifies whether this is a GPT
adjoint calculation. The }(hL) — This keyword specifies whether this is a GPT
adjoint calculation. The h j2hhh!NhNubj)}(h*gpt*h]h/gpt}(hhh j3ubah}(h]h]h]h]h]uhjh j2ubh/6 keyword is active only for adjoint
calculations. [no]}(h6 keyword is active only for adjoint
calculations. [no]h j2hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMXh jg2hhubj))}(hThe TRITON control module automatically sets the values for forward,
adjoint, and gpt keywords; therefore, they can typically be omitted from
the Parameter Block. Default values are recommended unless running
stand-alone NEWT adjoint calculations.h]hM)}(hThe TRITON control module automatically sets the values for forward,
adjoint, and gpt keywords; therefore, they can typically be omitted from
the Parameter Block. Default values are recommended unless running
stand-alone NEWT adjoint calculations.h]h/The TRITON control module automatically sets the values for forward,
adjoint, and gpt keywords; therefore, they can typically be omitted from
the Parameter Block. Default values are recommended unless running
stand-alone NEWT adjoint calculations.}(hj!3h j3ubah}(h]h]h]h]h]uhhLh!h"hM\h j3ubah}(h]h]h]h]h]uhj)h jg2hhh!h"hNubhM)}(hX**run=**\ (*yes/no*) — A run=no calculation will perform all setup
calculations normally performed before beginning iterations and then
will stop. It is useful for debugging input and obtaining plots of the
input geometry. Run=yes will perform a complete calculation. [yes]h](h)}(h**run=**h]h/run=}(hhh j73ubah}(h]h]h]h]h]uhhh j33ubh/ (}(h\ (h j33hhh!NhNubj)}(h*yes/no*h]h/yes/no}(hhh jJ3ubah}(h]h]h]h]h]uhjh j33ubh/X) — A run=no calculation will perform all setup
calculations normally performed before beginning iterations and then
will stop. It is useful for debugging input and obtaining plots of the
input geometry. Run=yes will perform a complete calculation. [yes]}(hX) — A run=no calculation will perform all setup
calculations normally performed before beginning iterations and then
will stop. It is useful for debugging input and obtaining plots of the
input geometry. Run=yes will perform a complete calculation. [yes]h j33hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMah jg2hhubhM)}(hX**premix=**\ (*yes/no*) — This flag indicates whether the cross section
library contains microscopic (premix=no) or macroscopic (premix=yes)
cross sections. In essence, it creates a mixing table with a mixture
fraction of 1.0 for each mixture on the library. Other mixing tables are
ignored. The premixed cross section option is active only for
stand-alone NEWT calculations. [no]h](h)}(h**premix=**h]h/premix=}(hhh jg3ubah}(h]h]h]h]h]uhhh jc3ubh/ (}(h\ (h jc3hhh!NhNubj)}(h*yes/no*h]h/yes/no}(hhh jz3ubah}(h]h]h]h]h]uhjh jc3ubh/Xi) — This flag indicates whether the cross section
library contains microscopic (premix=no) or macroscopic (premix=yes)
cross sections. In essence, it creates a mixing table with a mixture
fraction of 1.0 for each mixture on the library. Other mixing tables are
ignored. The premixed cross section option is active only for
stand-alone NEWT calculations. [no]}(hXi) — This flag indicates whether the cross section
library contains microscopic (premix=no) or macroscopic (premix=yes)
cross sections. In essence, it creates a mixing table with a mixture
fraction of 1.0 for each mixture on the library. Other mixing tables are
ignored. The premixed cross section option is active only for
stand-alone NEWT calculations. [no]h jc3hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMfh jg2hhubhM)}(h**kguess=**\ (*RN*) — Initial guess at eigenvalue for an eigenvalue
calculation. This parameter may be entered but is not used if a source
calculation is performed or a restart file is used to determine the
initial guess. [1.0]h](h)}(h**kguess=**h]h/kguess=}(hhh j3ubah}(h]h]h]h]h]uhhh j3ubh/ (}(h\ (h j3hhh!NhNubj)}(h*RN*h]h/RN}(hhh j3ubah}(h]h ]h]h]h]uhjh j3ubh/) — Initial guess at eigenvalue for an eigenvalue
calculation. This parameter may be entered but is not used if a source
calculation is performed or a restart file is used to determine the
initial guess. [1.0]}(h) — Initial guess at eigenvalue for an eigenvalue
calculation. This parameter may be entered but is not used if a source
calculation is performed or a restart file is used to determine the
initial guess. [1.0]h j3hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMmh jg2hhubhM)}(hXs**restart=**\ (*yes/no*) — If restart=yes is specified, NEWT will open
file *restart_newt* and read scalar fluxes and fission rates, enabling a
restart from the point at which a previous calculation ended. The file
*restart_newt* is always written by NEWT at the end of every successful
calculation. The code assumes that all geometry is unchanged from the
previous calculation but does allow restart with a different angular
quadrature set and P\ :sub:`n` scattering coefficients. A low-order
solution can be used to accelerate a higher-order solution by restarting
using the converged flux of the lower-order solution. [no]h](h)}(h**restart=**h]h/restart=}(hhh j3ubah}(h]h]h]h]h]uhhh j3ubh/ (}(h\ (h j3hhh!NhNubj)}(h*yes/no*h]h/yes/no}(hhh j3ubah}(h]h]h]h]h]uhjh j3ubh/7) — If restart=yes is specified, NEWT will open
file }(h7) — If restart=yes is specified, NEWT will open
file h j3hhh!NhNubj)}(h*restart_newt*h]h/restart_newt}(hhh j3ubah}(h]h]h]h]h]uhjh j3ubh/} and read scalar fluxes and fission rates, enabling a
restart from the point at which a previous calculation ended. The file
}(h} and read scalar fluxes and fission rates, enabling a
restart from the point at which a previous calculation ended. The file
h j3hhh!NhNubj)}(h*restart_newt*h]h/restart_newt}(hhh j4ubah}(h]h]h]h]h]uhjh j3ubh/ is always written by NEWT at the end of every successful
calculation. The code assumes that all geometry is unchanged from the
previous calculation but does allow restart with a different angular
quadrature set and P }(h is always written by NEWT at the end of every successful
calculation. The code assumes that all geometry is unchanged from the
previous calculation but does allow restart with a different angular
quadrature set and P\ h j3hhh!NhNubj)}(h:sub:`n`h]h/n}(hhh j4ubah}(h]h]h]h]h]uhjh j3ubh/ scattering coefficients. A low-order
solution can be used to accelerate a higher-order solution by restarting
using the converged flux of the lower-order solution. [no]}(h scattering coefficients. A low-order
solution can be used to accelerate a higher-order solution by restarting
using the converged flux of the lower-order solution. [no]h j3hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMrh jg2hhubhM)}(h**savrest=**\ (*yes/no*) — Determines whether or not a geometry restart
file *worf* is written at the end of a calculation. If written, it will
overwrite any existing geometry restart file. [yes]h](h)}(h**savrest=**h]h/savrest=}(hhh j04ubah}(h]h]h]h]h]uhhh j,4ubh/ (}(h\ (h j,4hhh!NhNubj)}(h*yes/no*h]h/yes/no}(hhh jC4ubah}(h]h]h]h]h]uhjh j,4ubh/8) — Determines whether or not a geometry restart
file }(h8) — Determines whether or not a geometry restart
file h j,4hhh!NhNubj)}(h*worf*h]h/worf}(hhh jV4ubah}(h]h]h]h]h]uhjh j,4ubh/q is written at the end of a calculation. If written, it will
overwrite any existing geometry restart file. [yes]}(hq is written at the end of a calculation. If written, it will
overwrite any existing geometry restart file. [yes]h j,4hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM|h jg2hhubj))}(hXThe default values of savrest and kguess are recommended. The TRITON
control module automates generation and reuse of the geometry restart
file, as well as the initial guess of the eigenvalue. Keywords run,
premix, and restart can generally be omitted unless the following
conditions are applicable:
- TRITON T-NEWT sequence calculation or stand-alone NEWT calculation
with user-supplied restart file, restart=yes.
- Stand-alone NEWT calculation with user-supplied premixed cross
section file, premix=yes.
- Interested only in performing setup calculations to debug input and
generate geometry plots, run=no, and/or PARM=CHECK in the TRITON
sequence input.h](hM)}(hX+The default values of savrest and kguess are recommended. The TRITON
control module automates generation and reuse of the geometry restart
file, as well as the initial guess of the eigenvalue. Keywords run,
premix, and restart can generally be omitted unless the following
conditions are applicable:h]h/X+The default values of savrest and kguess are recommended. The TRITON
control module automates generation and reuse of the geometry restart
file, as well as the initial guess of the eigenvalue. Keywords run,
premix, and restart can generally be omitted unless the following
conditions are applicable:}(hju4h js4ubah}(h]h]h]h]h]uhhLh!h"hMh jo4ubh bullet_list)}(hhh](h@)}(hqTRITON T-NEWT sequence calculation or stand-alone NEWT calculation
with user-supplied restart file, restart=yes.
h]hM)}(hpTRITON T-NEWT sequence calculation or stand-alone NEWT calculation
with user-supplied restart file, restart=yes.h]h/pTRITON T-NEWT sequence calculation or stand-alone NEWT calculation
with user-supplied restart file, restart=yes.}(hj4h j4ubah}(h]h]h]h]h]uhhLh!h"hMh j4ubah}(h]h]h]h]h]uhh?h j4ubh@)}(hYStand-alone NEWT calculation with user-supplied premixed cross
section file, premix=yes.
h]hM)}(hXStand-alone NEWT calculation with user-supplied premixed cross
section file, premix=yes.h]h/XStand-alone NEWT calculation with user-supplied premixed cross
section file, premix=yes.}(hj4h j4ubah}(h]h]h]h]h]uhhLh!h"hMh j4ubah}(h]h]h]h]h]uhh?h j4ubh@)}(hInterested only in performing setup calculations to debug input and
generate geometry plots, run=no, and/or PARM=CHECK in the TRITON
sequence input.h]hM)}(hInterested only in performing setup calculations to debug input and
generate geometry plots, run=no, and/or PARM=CHECK in the TRITON
sequence input.h]h/Interested only in performing setup calculations to debug input and
generate geometry plots, run=no, and/or PARM=CHECK in the TRITON
sequence input.}(hj4h j4ubah}(h]h]h]h]h]uhhLh!h"hMh j4ubah}(h]h]h]h]h]uhh?h j4ubeh}(h]h]h]h]h]bullet-uhj4h!h"hMh jo4ubeh}(h]h]h]h]h]uhj)h jg2hhh!NhNubhM)}(hXc**solntype**\ =(keff/b1/src) — Specifies solution mode type: keff is
eigenvalue, b1 is eigenvalue mode followed by a buckling correction, and
src is fixed source (no eigenvalue calculation). Fixed source
calculations require additional data for the source specification (see
Materials and Source data blocks in :ref:`9-2-3-3` and :ref:`9-2-3-4`). [keff]h](h)}(h**solntype**h]h/solntype}(hhh j4ubah}(h]h]h]h]h]uhhh j4ubh/X- =(keff/b1/src) — Specifies solution mode type: keff is
eigenvalue, b1 is eigenvalue mode followed by a buckling correction, and
src is fixed source (no eigenvalue calculation). Fixed source
calculations require additional data for the source specification (see
Materials and Source data blocks in }(hX-\ =(keff/b1/src) — Specifies solution mode type: keff is
eigenvalue, b1 is eigenvalue mode followed by a buckling correction, and
src is fixed source (no eigenvalue calculation). Fixed source
calculations require additional data for the source specification (see
Materials and Source data blocks in h j4hhh!NhNubj)}(h:ref:`9-2-3-3`h]j)}(hj4h]h/9-2-3-3}(hhh j4ubah}(h]h](jEstdstd-refeh]h]h]uhjh j4ubah}(h]h]h]h]h]refdochj refdomainj5reftyperefrefexplicitrefwarnjW9-2-3-3uhjh!h"hMh j4ubh/ and }(h and h j4hhh!NhNubj)}(h:ref:`9-2-3-4`h]j)}(hj5h]h/9-2-3-4}(hhh j5ubah}(h]h](jEstdstd-refeh]h]h]uhjh j5ubah}(h]h]h]h]h]refdochj refdomainj&5reftyperefrefexplicitrefwarnjW9-2-3-4uhjh!h"hMh j4ubh/ ). [keff]}(h ). [keff]h j4hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jg2hhubhM)}(hX**collapse=**\ (*yes/no*) — If collapse=yes is specified, a
flux-weighted collapse is performed by material number; cross sections
for each nuclide in each material in the problem are collapsed to a
specified (or default) group structure based on the average flux in that
material. If collapse=yes, NEWT will look for the *collapse* parameter
block; if not found, NEWT will generate cross sections based on the
original group structure. If a Homogenization block is present, then
collapse is always set to yes. [no]h](h)}(h
**collapse=**h]h/ collapse=}(hhh jG5ubah}(h]h]h]h]h]uhhh jC5ubh/ (}(h\ (h jC5hhh!NhNubj)}(h*yes/no*h]h/yes/no}(hhh jZ5ubah}(h]h]h]h]h]uhjh jC5ubh/X.) — If collapse=yes is specified, a
flux-weighted collapse is performed by material number; cross sections
for each nuclide in each material in the problem are collapsed to a
specified (or default) group structure based on the average flux in that
material. If collapse=yes, NEWT will look for the }(hX.) — If collapse=yes is specified, a
flux-weighted collapse is performed by material number; cross sections
for each nuclide in each material in the problem are collapsed to a
specified (or default) group structure based on the average flux in that
material. If collapse=yes, NEWT will look for the h jC5hhh!NhNubj)}(h
*collapse*h]h/collapse}(hhh jm5ubah}(h]h]h]h]h]uhjh jC5ubh/ parameter
block; if not found, NEWT will generate cross sections based on the
original group structure. If a Homogenization block is present, then
collapse is always set to yes. [no]}(h parameter
block; if not found, NEWT will generate cross sections based on the
original group structure. If a Homogenization block is present, then
collapse is always set to yes. [no]h jC5hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jg2hhubhM)}(hX**saveangflx=**\ (*yes/no*) — Option to save angular flux solution. The
angular flux is saved to a binary file used in the TSUNAMI-2D sequence
of the TRITON control module. Because the angular flux can require
significant file storage, it is not saved by default. The angular flux
solution can and should be saved for TSUNAMI-2D calculations to generate
more accurate sensitivity coefficients. [no]h](h)}(h**saveangflx=**h]h/saveangflx=}(hhh j5ubah}(h]h]h]h]h]uhhh j5ubh/ (}(h\ (h j5hhh!NhNubj)}(h*yes/no*h]h/yes/no}(hhh j5ubah}(h]h]h]h]h]uhjh j5ubh/Xv) — Option to save angular flux solution. The
angular flux is saved to a binary file used in the TSUNAMI-2D sequence
of the TRITON control module. Because the angular flux can require
significant file storage, it is not saved by default. The angular flux
solution can and should be saved for TSUNAMI-2D calculations to generate
more accurate sensitivity coefficients. [no]}(hXv) — Option to save angular flux solution. The
angular flux is saved to a binary file used in the TSUNAMI-2D sequence
of the TRITON control module. Because the angular flux can require
significant file storage, it is not saved by default. The angular flux
solution can and should be saved for TSUNAMI-2D calculations to generate
more accurate sensitivity coefficients. [no]h j5hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jg2hhubj))}(hXKeyword threads should be omitted in favor of the SCALE command line–I
option. Keywords solntype, collapse, and saveangflx should be omitted
unless the following conditions are applicable.
- For homogenized few-group cross section generation for nodal
calculations, solntype* *should be b1. This option will perform a
critical spectrum calculation, which will be folded into cross
section homogenization calculation. The critical spectrum is also
folded into the generation of ADFs and reaction rates for
depletion calculations.
- Generation of a new collapsed cross section library, collapse=yes.
- For TSUNAMI-2D calculations, saveangflx=yes.h](hM)}(hKeyword threads should be omitted in favor of the SCALE command line–I
option. Keywords solntype, collapse, and saveangflx should be omitted
unless the following conditions are applicable.h]h/Keyword threads should be omitted in favor of the SCALE command line–I
option. Keywords solntype, collapse, and saveangflx should be omitted
unless the following conditions are applicable.}(hj5h j5ubah}(h]h]h]h]h]uhhLh!h"hMh j5ubj4)}(hhh](h@)}(hXRFor homogenized few-group cross section generation for nodal
calculations, solntype* *should be b1. This option will perform a
critical spectrum calculation, which will be folded into cross
section homogenization calculation. The critical spectrum is also
folded into the generation of ADFs and reaction rates for
depletion calculations.
h]hM)}(hXQFor homogenized few-group cross section generation for nodal
calculations, solntype* *should be b1. This option will perform a
critical spectrum calculation, which will be folded into cross
section homogenization calculation. The critical spectrum is also
folded into the generation of ADFs and reaction rates for
depletion calculations.h](h/UFor homogenized few-group cross section generation for nodal
calculations, solntype* }(hUFor homogenized few-group cross section generation for nodal
calculations, solntype* h j5ubj*)}(hj,h]h/*}(hhh j5ubah}(h]id57ah]h]h]h]refidid56uhj*h j5ubh/should be b1. This option will perform a
critical spectrum calculation, which will be folded into cross
section homogenization calculation. The critical spectrum is also
folded into the generation of ADFs and reaction rates for
depletion calculations.}(hshould be b1. This option will perform a
critical spectrum calculation, which will be folded into cross
section homogenization calculation. The critical spectrum is also
folded into the generation of ADFs and reaction rates for
depletion calculations.h j5ubeh}(h]h]h]h]h]uhhLh!h"hMh j5ubah}(h]h]h]h]h]uhh?h j5ubh@)}(hCGeneration of a new collapsed cross section library, collapse=yes.
h]hM)}(hBGeneration of a new collapsed cross section library, collapse=yes.h]h/BGeneration of a new collapsed cross section library, collapse=yes.}(hj5h j5ubah}(h]h]h]h]h]uhhLh!h"hMh j5ubah}(h]h]h]h]h]uhh?h j5ubh@)}(h,For TSUNAMI-2D calculations, saveangflx=yes.h]hM)}(hj6h]h/,For TSUNAMI-2D calculations, saveangflx=yes.}(hj6h j6ubah}(h]h]h]h]h]uhhLh!h"hMh j6ubah}(h]h]h]h]h]uhh?h j5ubeh}(h]h]h]h]h]j4j4uhj4h!h"hMh j5ubeh}(h]h]h]h]h]uhj)h jg2hhh!NhNubh)}(h.. _9-2-3-2-5:h]h}(h]h]h]h]h]hid58uhh
hMh jg2hhh!h"ubh$)}(hhh](h))}(hGeometry processing optionsh]h/Geometry processing options}(hjD6h jB6hhh!NhNubah}(h]h]h]h]h]uhh(h j?6hhh!h"hMubhM)}(hX^**combine**\ =(\ *yes/no*) — Automatic grid generation can result in
very small grid cells in some locations. Setting parameter combine to
*yes* performs automatic combination of smaller grid cells into adjacent
neighbor of same material, if possible. Combine is automatically set to
*no* if CMFD is enabled; this setting cannot be overridden. [no]h](h)}(h**combine**h]h/combine}(hhh jT6ubah}(h]h]h]h]h]uhhh jP6ubh/ =( }(h\ =(\ h jP6hhh!NhNubj)}(h*yes/no*h]h/yes/no}(hhh jg6ubah}(h]h]h]h]h]uhjh jP6ubh/t) — Automatic grid generation can result in
very small grid cells in some locations. Setting parameter combine to
}(ht) — Automatic grid generation can result in
very small grid cells in some locations. Setting parameter combine to
h jP6hhh!NhNubj)}(h*yes*h]h/yes}(hhh jz6ubah}(h]h]h]h]h]uhjh jP6ubh/ performs automatic combination of smaller grid cells into adjacent
neighbor of same material, if possible. Combine is automatically set to
}(h performs automatic combination of smaller grid cells into adjacent
neighbor of same material, if possible. Combine is automatically set to
h jP6hhh!NhNubj)}(h*no*h]h/no}(hhh j6ubah}(h]h]h]h]h]uhjh jP6ubh/< if CMFD is enabled; this setting cannot be overridden. [no]}(h< if CMFD is enabled; this setting cannot be overridden. [no]h jP6hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j?6hhubhM)}(hX**clearint**\ =(\ *yes/no*) — Grid generation option that removes the
global NEWT grid if a local unit grid is supplied. (For meshing options,
see the *boundary* keyword in the Geometry block description in
:ref:`9-2-3-6`) By default, clearint is set to yes, which means the
global grid is removed if local grids are provided. If CMFD acceleration
is enabled, clearint is set to no, which means both the global grid and
optional local grids are used. [yes]h](h)}(h**clearint**h]h/clearint}(hhh j6ubah}(h]h]h]h]h]uhhh j6ubh/ =( }(h\ =(\ h j6hhh!NhNubj)}(h*yes/no*h]h/yes/no}(hhh j6ubah}(h]h]h]h]h]uhjh j6ubh/) — Grid generation option that removes the
global NEWT grid if a local unit grid is supplied. (For meshing options,
see the }(h) — Grid generation option that removes the
global NEWT grid if a local unit grid is supplied. (For meshing options,
see the h j6hhh!NhNubj)}(h
*boundary*h]h/boundary}(hhh j6ubah}(h]h]h]h]h]uhjh j6ubh/. keyword in the Geometry block description in
}(h. keyword in the Geometry block description in
h j6hhh!NhNubj)}(h:ref:`9-2-3-6`h]j)}(hj6h]h/9-2-3-6}(hhh j6ubah}(h]h](jEstdstd-refeh]h]h]uhjh j6ubah}(h]h]h]h]h]refdochj refdomainj6reftyperefrefexplicitrefwarnjW9-2-3-6uhjh!h"hMh j6ubh/) By default, clearint is set to yes, which means the
global grid is removed if local grids are provided. If CMFD acceleration
is enabled, clearint is set to no, which means both the global grid and
optional local grids are used. [yes]}(h) By default, clearint is set to yes, which means the
global grid is removed if local grids are provided. If CMFD acceleration
is enabled, clearint is set to no, which means both the global grid and
optional local grids are used. [yes]h j6hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j?6hhubhM)}(h**grid_tol=**\ (*RN*) — Tolerance used in determining if polygon
vertices are numerically identical during NEWT grid generation.
[0.000001]h](h)}(h
**grid_tol=**h]h/ grid_tol=}(hhh j7ubah}(h]h]h]h]h]uhhh j7ubh/ (}(h\ (h j7hhh!NhNubj)}(h*RN*h]h/RN}(hhh j%7ubah}(h]h]h]h]h]uhjh j7ubh/y) — Tolerance used in determining if polygon
vertices are numerically identical during NEWT grid generation.
[0.000001]}(hy) — Tolerance used in determining if polygon
vertices are numerically identical during NEWT grid generation.
[0.000001]h j7hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j?6hhubhM)}(h**cell_tol=**\ (*RN*) — Tolerance used in determining if polygon
vertices are numerically identical during NEWT cell generation.
[0.000001]h](h)}(h
**cell_tol=**h]h/ cell_tol=}(hhh jB7ubah}(h]h]h]h]h]uhhh j>7ubh/ (}(h\ (h j>7hhh!NhNubj)}(h*RN*h]h/RN}(hhh jU7ubah}(h]h]h]h]h]uhjh j>7ubh/y) — Tolerance used in determining if polygon
vertices are numerically identical during NEWT cell generation.
[0.000001]}(hy) — Tolerance used in determining if polygon
vertices are numerically identical during NEWT cell generation.
[0.000001]h j>7hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j?6hhubhM)}(h**line_tol=**\ (*RN*) — Tolerance used in determining if polygon
vertices are numerically identical during NEWT line generation.
[1.0e-10]h](h)}(h
**line_tol=**h]h/ line_tol=}(hhh jr7ubah}(h]h]h]h]h]uhhh jn7ubh/ (}(h\ (h jn7hhh!NhNubj)}(h*RN*h]h/RN}(hhh j7ubah}(h]h]h]h]h]uhjh jn7ubh/x) — Tolerance used in determining if polygon
vertices are numerically identical during NEWT line generation.
[1.0e-10]}(hx) — Tolerance used in determining if polygon
vertices are numerically identical during NEWT line generation.
[1.0e-10]h jn7hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j?6hhubj))}(hX0The default values for all geometry-processing keywords are recommended
and can be omitted. For problems with very fine mesh, tighter grid and
cell tolerances should be applied. For problems that terminate with a
ray-tracing error (i.e., tracer error), tighter grid and cell tolerances
should be applied.h]hM)}(hX0The default values for all geometry-processing keywords are recommended
and can be omitted. For problems with very fine mesh, tighter grid and
cell tolerances should be applied. For problems that terminate with a
ray-tracing error (i.e., tracer error), tighter grid and cell tolerances
should be applied.h]h/X0The default values for all geometry-processing keywords are recommended
and can be omitted. For problems with very fine mesh, tighter grid and
cell tolerances should be applied. For problems that terminate with a
ray-tracing error (i.e., tracer error), tighter grid and cell tolerances
should be applied.}(hj7h j7ubah}(h]h]h]h]h]uhhLh!h"hMh j7ubah}(h]h]h]h]h]uhj)h j?6hhh!h"hNubh)}(h.. _9-2-3-2-6:h]h}(h]h]h]h]h]hid59uhh
hMh j?6hhh!h"ubeh}(h](geometry-processing-optionsj>6eh]h](geometry processing options 9-2-3-2-5eh]h]uhh#h jg2hhh!h"hMj}j7j46sj}j>6j46subeh}(h](control-optionsj[2eh]h] 9-2-3-2-4ah]control optionsah]uhh#h j$hhh!h"hMOjKj}j7jQ2sj}j[2jQ2subh$)}(hhh](h))}(hCritical spectrum optionsh]h/Critical spectrum options}(hj7h j7hhh!NhNubah}(h]h]h]h]h]uhh(h j7hhh!h"hMubhM)}(h**useb1**\ =(\ *yes/no*) —Turns on/off the use of the B1 approximation
to determine the critical spectrum. If useb1 is set to no, the P1
approximation is used. [yes]h](h)}(h **useb1**h]h/useb1}(hhh j7ubah}(h]h]h]h]h]uhhh j7ubh/ =( }(h\ =(\ h j7hhh!NhNubj)}(h*yes/no*h]h/yes/no}(hhh j7ubah}(h]h]h]h]h]uhjh j7ubh/) —Turns on/off the use of the B1 approximation
to determine the critical spectrum. If useb1 is set to no, the P1
approximation is used. [yes]}(h) —Turns on/off the use of the B1 approximation
to determine the critical spectrum. If useb1 is set to no, the P1
approximation is used. [yes]h j7hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j7hhubhM)}(hO**b2=**\ (*RN*) — Material buckling factor, in units of 1/cm\ :sup:`2`.
[0.0]h](h)}(h**b2=**h]h/b2=}(hhh j8ubah}(h]h]h]h]h]uhhh j8ubh/ (}(h\ (h j8hhh!NhNubj)}(h*RN*h]h/RN}(hhh j/8ubah}(h]h]h]h]h]uhjh j8ubh/2) — Material buckling factor, in units of 1/cm }(h2) — Material buckling factor, in units of 1/cm\ h j8hhh!NhNubjY)}(h:sup:`2`h]h/2}(hhh jB8ubah}(h]h]h]h]h]uhjXh j8ubh/.
[0.0]}(h.
[0.0]h j8hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j7hhubhM)}(hX&**height=**\ (*RN*) — Height (transverse dimension) in centimeters. Used
in a geometric buckling correction to calculate leakage normal to the
plane of the input 2-D model. Keywords **dz=** and **deltaz=** are
equivalent. When set to zero (default), no buckling correction is
performed. [0.0]h](h)}(h**height=**h]h/height=}(hhh j_8ubah}(h]h]h]h]h]uhhh j[8ubh/ (}(h\ (h j[8hhh!NhNubj)}(h*RN*h]h/RN}(hhh jr8ubah}(h]h]h]h]h]uhjh j[8ubh/) — Height (transverse dimension) in centimeters. Used
in a geometric buckling correction to calculate leakage normal to the
plane of the input 2-D model. Keywords }(h) — Height (transverse dimension) in centimeters. Used
in a geometric buckling correction to calculate leakage normal to the
plane of the input 2-D model. Keywords h j[8hhh!NhNubh)}(h**dz=**h]h/dz=}(hhh j8ubah}(h]h]h]h]h]uhhh j[8ubh/ and }(h and h j[8hhh!NhNubh)}(h**deltaz=**h]h/deltaz=}(hhh j8ubah}(h]h]h]h]h]uhhh j[8ubh/W are
equivalent. When set to zero (default), no buckling correction is
performed. [0.0]}(hW are
equivalent. When set to zero (default), no buckling correction is
performed. [0.0]h j[8hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j7hhubhM)}(h**bf=**\ (*RN*) — Twice the extrapolation distance multiplier used to
determine the geometric buckling correction. [1.420892]h](h)}(h**bf=**h]h/bf=}(hhh j8ubah}(h]h]h]h]h]uhhh j8ubh/ (}(h\ (h j8hhh!NhNubj)}(h*RN*h]h/RN}(hhh j8ubah}(h]h]h]h]h]uhjh j8ubh/q) — Twice the extrapolation distance multiplier used to
determine the geometric buckling correction. [1.420892]}(hq) — Twice the extrapolation distance multiplier used to
determine the geometric buckling correction. [1.420892]h j8hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j7hhubj))}(hX^If critical spectrum corrections are to be applied, the default values
listed above are recommended along with **solntype=b1**\ . In this
option, NEWT will search for the material buckling value such that the
homogenized infinite-medium system is critical. NEWT currently uses the
B1 approximation as the default. If the P1 approximation is preferred,
useb1should be set to no. The infinite-medium B1 (or P1) buckling search
is performed in the energy group structure as the original model.
Alternatively, the user can supply the material buckling value using
the b2 keyword, and specifying the B1 (default) or P1
approximation ( **useb1=no** ). In this
case, **solntype** should be set to **keff**\ .
Alternatively, if the user knows the transverse dimension, a geometry
buckling factor can be applied, derived from the
user-defined **height** and extrapolation distance
term **bf** as the following:
:math:`B_{g}^{2}=\left(\frac{\pi}{H+z / \sigma_{t r}}\right)^{2}`
In this formula, H is keyword height, z is keyword bf, and :math:`\sigma_{t r}` is the
collapsed, homogenized macroscopic transport cross section.h](hM)}(hXIf critical spectrum corrections are to be applied, the default values
listed above are recommended along with **solntype=b1**\ . In this
option, NEWT will search for the material buckling value such that the
homogenized infinite-medium system is critical. NEWT currently uses the
B1 approximation as the default. If the P1 approximation is preferred,
useb1should be set to no. The infinite-medium B1 (or P1) buckling search
is performed in the energy group structure as the original model.h](h/oIf critical spectrum corrections are to be applied, the default values
listed above are recommended along with }(hoIf critical spectrum corrections are to be applied, the default values
listed above are recommended along with h j8ubh)}(h**solntype=b1**h]h/solntype=b1}(hhh j8ubah}(h]h]h]h]h]uhhh j8ubh/Xl . In this
option, NEWT will search for the material buckling value such that the
homogenized infinite-medium system is critical. NEWT currently uses the
B1 approximation as the default. If the P1 approximation is preferred,
useb1should be set to no. The infinite-medium B1 (or P1) buckling search
is performed in the energy group structure as the original model.}(hXl\ . In this
option, NEWT will search for the material buckling value such that the
homogenized infinite-medium system is critical. NEWT currently uses the
B1 approximation as the default. If the P1 approximation is preferred,
useb1should be set to no. The infinite-medium B1 (or P1) buckling search
is performed in the energy group structure as the original model.h j8ubeh}(h]h]h]h]h]uhhLh!h"hMh j8ubhM)}(hAlternatively, the user can supply the material buckling value using
the b2 keyword, and specifying the B1 (default) or P1
approximation ( **useb1=no** ). In this
case, **solntype** should be set to **keff**\ .h](h/Alternatively, the user can supply the material buckling value using
the b2 keyword, and specifying the B1 (default) or P1
approximation ( }(hAlternatively, the user can supply the material buckling value using
the b2 keyword, and specifying the B1 (default) or P1
approximation ( h j9ubh)}(h**useb1=no**h]h/useb1=no}(hhh j9ubah}(h]h]h]h]h]uhhh j9ubh/ ). In this
case, }(h ). In this
case, h j9ubh)}(h**solntype**h]h/solntype}(hhh j#9ubah}(h]h]h]h]h]uhhh j9ubh/ should be set to }(h should be set to h j9ubh)}(h**keff**h]h/keff}(hhh j69ubah}(h]h]h]h]h]uhhh j9ubh/ .}(h\ .h j9ubeh}(h]h]h]h]h]uhhLh!h"hMh j8ubhM)}(hAlternatively, if the user knows the transverse dimension, a geometry
buckling factor can be applied, derived from the
user-defined **height** and extrapolation distance
term **bf** as the following:h](h/Alternatively, if the user knows the transverse dimension, a geometry
buckling factor can be applied, derived from the
user-defined }(hAlternatively, if the user knows the transverse dimension, a geometry
buckling factor can be applied, derived from the
user-defined h jO9ubh)}(h
**height**h]h/height}(hhh jX9ubah}(h]h]h]h]h]uhhh jO9ubh/! and extrapolation distance
term }(h! and extrapolation distance
term h jO9ubh)}(h**bf**h]h/bf}(hhh jk9ubah}(h]h]h]h]h]uhhh jO9ubh/ as the following:}(h as the following:h jO9ubeh}(h]h]h]h]h]uhhLh!h"hMh j8ubhM)}(hA:math:`B_{g}^{2}=\left(\frac{\pi}{H+z / \sigma_{t r}}\right)^{2}`h]jY)}(hA:math:`B_{g}^{2}=\left(\frac{\pi}{H+z / \sigma_{t r}}\right)^{2}`h]h/9B_{g}^{2}=\left(\frac{\pi}{H+z / \sigma_{t r}}\right)^{2}}(hhh j9ubah}(h]h]h]h]h]uhjXh j9ubah}(h]h]h]h]h]uhhLh!h"hMh j8ubhM)}(hIn this formula, H is keyword height, z is keyword bf, and :math:`\sigma_{t r}` is the
collapsed, homogenized macroscopic transport cross section.h](h/;In this formula, H is keyword height, z is keyword bf, and }(h;In this formula, H is keyword height, z is keyword bf, and h j9ubjY)}(h:math:`\sigma_{t r}`h]h/\sigma_{t r}}(hhh j9ubah}(h]h]h]h]h]uhjXh j9ubh/C is the
collapsed, homogenized macroscopic transport cross section.}(hC is the
collapsed, homogenized macroscopic transport cross section.h j9ubeh}(h]h]h]h]h]uhhLh!h"hMh j8ubeh}(h]h]h]h]h]uhj)h j7hhh!h"hNubh)}(h.. _9-2-3-2-7:h]h}(h]h]h]h]h]hid60uhh
hMh j7hhh!h"ubeh}(h](critical-spectrum-optionsj7eh]h](critical spectrum options 9-2-3-2-6eh]h]uhh#h j$hhh!h"hMj}j9j7sj}j7j7subh$)}(hhh](h))}(hFile unit optionsh]h/File unit options}(hj9h j9hhh!NhNubah}(h]h]h]h]h]uhh(h j9hhh!h"hM ubj))}(hX!It is highly recommended that the file unit options below be omitted or
that default values be used. Alternate file unit values are acceptable
for stand-alone NEWT calculations, but changing their values may
adversely impact other SCALE modules if NEWT is invoked through a SCALE
sequence.h]hM)}(hX!It is highly recommended that the file unit options below be omitted or
that default values be used. Alternate file unit values are acceptable
for stand-alone NEWT calculations, but changing their values may
adversely impact other SCALE modules if NEWT is invoked through a SCALE
sequence.h]h/X!It is highly recommended that the file unit options below be omitted or
that default values be used. Alternate file unit values are acceptable
for stand-alone NEWT calculations, but changing their values may
adversely impact other SCALE modules if NEWT is invoked through a SCALE
sequence.}(hj9h j9ubah}(h]h]h]h]h]uhhLh!h"hMh j9ubah}(h]h]h]h]h]uhj)h j9hhh!h"hNubhM)}(h**hmoglib=**\ (*IN, 0uhjGh!h"hM0h j9hhubh)}(h.. _9-2-3-3:h]h}(h]h]h]h]h]hid62uhh
hM:h j9hhh!h"ubeh}(h](file-unit-optionsj9eh]h](file unit options 9-2-3-2-7eh]h]uhh#h j$hhh!h"hM j}j;j9sj}j9j9subeh}(h](parameter-blockj$eh]h](parameter block9-2-3-2eh]h]uhh#h jhhh!h"hM6j}j;j$sj}j$j$subh$)}(hhh](h))}(hMaterial Blockh]h/Material Block}(hj;h j;hhh!NhNubah}(h]h]h]h]h]uhh(h j;hhh!h"hM=ubhM)}(h6**Material block keyword = matl, material, materials**h]h)}(hj;h]h/2Material block keyword = matl, material, materials}(hhh j;ubah}(h]h]h]h]h]uhhh j;ubah}(h]h]h]h]h]uhhLh!h"hM?h j;hhubhM)}(hThe Material block is always required. Material data must be specified
for each mixture used in the calculation. The general format of the
Material block is as follows:h]h/The Material block is always required. Material data must be specified
for each mixture used in the calculation. The general format of the
Material block is as follows:}(hj;h j;hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMAh j;hhubjH)}(hTREAD materials
mix=M pn=N srcid=I com=’embedded comment’ end
END materialsh]h/TREAD materials
mix=M pn=N srcid=I com=’embedded comment’ end
END materials}(hhh j;ubah}(h]h]h]h]h]j=j>uhjGh!h"hMGh j;hhubhM)}(hwhereh]h/where}(hj;h j;hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMKh j;hhubjP)}(hhh](hM)}(hM = mixture ID;h]h/M = mixture ID;}(hj;h j;ubah}(h]h]h]h]h]uhhLh!h"hMMh j;ubhM)}(hGN = P\ :sub:`n` order for scattering in mixture M (by default, N is 1);h](h/N = P }(hN = P\ h j <ubj)}(h:sub:`n`h]h/n}(hhh j<ubah}(h]h]h]h]h]uhjh j <ubh/8 order for scattering in mixture M (by default, N is 1);}(h8 order for scattering in mixture M (by default, N is 1);h j <ubeh}(h]h]h]h]h]uhhLh!h"hMOh j;ubhM)}(heI = Source ID number (the source description for each source ID number
is given in the Source block).h]h/eI = Source ID number (the source description for each source ID number
is given in the Source block).}(hj-<h j+<ubah}(h]h]h]h]h]uhhLh!h"hMQh j;ubeh}(h]h]h]h]h]uhjOh j;hhh!h"hNubhM)}(hX{Up to 80 characters of text may be entered after *com=*, delimited by
single quotes (') or double quotes (''). A mixture specification is
required for each mixture used in the NEWT calculation. The order of the
keywords in each specification is unimportant, and only the mix= keyword
is required; however, each mixture specification **must** be terminated
by the **end** keyword.h](h/1Up to 80 characters of text may be entered after }(h1Up to 80 characters of text may be entered after h j?<hhh!NhNubj)}(h*com=*h]h/com=}(hhh jH<ubah}(h]h]h]h]h]uhjh j?<ubh/X, delimited by
single quotes (‘) or double quotes (‘’). A mixture specification is
required for each mixture used in the NEWT calculation. The order of the
keywords in each specification is unimportant, and only the mix= keyword
is required; however, each mixture specification }(hX, delimited by
single quotes (') or double quotes (''). A mixture specification is
required for each mixture used in the NEWT calculation. The order of the
keywords in each specification is unimportant, and only the mix= keyword
is required; however, each mixture specification h j?<hhh!NhNubh)}(h**must**h]h/must}(hhh j[<ubah}(h]h]h]h]h]uhhh j?<ubh/ be terminated
by the }(h be terminated
by the h j?<hhh!NhNubh)}(h**end**h]h/end}(hhh jn<ubah}(h]h]h]h]h]uhhh j?<ubh/ keyword.}(h keyword.h j?<hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMTh j;hhubhM)}(hX`A sample Material block is provided below for three different mixtures.
Each mixture is specified in a different manner to illustrate different
input formats. In this example, P3 scattering is applied in mixture 3,
and water and P1 are applied in the other mixtures. The pn= keyword is
omitted for mixture 1. The com= keyword is omitted for mixture 2.h]h/X`A sample Material block is provided below for three different mixtures.
Each mixture is specified in a different manner to illustrate different
input formats. In this example, P3 scattering is applied in mixture 3,
and water and P1 are applied in the other mixtures. The pn= keyword is
omitted for mixture 1. The com= keyword is omitted for mixture 2.}(hj<h j<hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM[h j;hhubjH)}(hsREAD materials
mix=3 pn=3 com='water' end
mix=1 com='3.0 enriched fuel' end
mix=2 pn=1 end
END materialsh]h/sREAD materials
mix=3 pn=3 com='water' end
mix=1 com='3.0 enriched fuel' end
mix=2 pn=1 end
END materials}(hhh j<ubah}(h]h]h]h]h]j=j>uhjGh!h"hMch j;hhubhM)}(hConsider this same set of mixtures but with a fixed source identified by source
ID 100 in mixture 1. This specification could be written as follows:h]h/Consider this same set of mixtures but with a fixed source identified by source
ID 100 in mixture 1. This specification could be written as follows:}(hj<h j<hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMih j;hhubjH)}(hREAD materials
mix=3 pn=3 com='water' end
com='3.0 enriched fuel' mix=1 pn=1 srcid=100 end
pn=1 mix=2 end
END materialsh]h/READ materials
mix=3 pn=3 com='water' end
com='3.0 enriched fuel' mix=1 pn=1 srcid=100 end
pn=1 mix=2 end
END materials}(hhh j<ubah}(h]h]h]h]h]j=j>uhjGh!h"hMnh j;hhubh)}(h.. _9-2-3-4:h]h}(h]h]h]h]h]hid63uhh
hMth j;hhh!h"ubeh}(h](material-blockj;eh]h](material block9-2-3-3eh]h]uhh#h jhhh!h"hM=j}j<j;sj}j;j;subh$)}(hhh](h))}(hSource blockh]h/Source block}(hj<h j<hhh!NhNubah}(h]h]h]h]h]uhh(h j<hhh!h"hMwubhM)}(h$**Source block keyword=source, src**h]h)}(hj<h]h/ Source block keyword=source, src}(hhh j<ubah}(h]h]h]h]h]uhhh j<ubah}(h]h]h]h]h]uhhLh!h"hMyh j<hhubhM)}(hThe Source block contains source strength specifications associated with
a given source ID. The source is assigned to a mixture via the srcid=
keyword in the Material block (:ref:`9-2-3-3`). Data are input using a
keyword-based format:h](h/The Source block contains source strength specifications associated with
a given source ID. The source is assigned to a mixture via the srcid=
keyword in the Material block (}(hThe Source block contains source strength specifications associated with
a given source ID. The source is assigned to a mixture via the srcid=
keyword in the Material block (h j<hhh!NhNubj)}(h:ref:`9-2-3-3`h]j)}(hj=h]h/9-2-3-3}(hhh j
=ubah}(h]h](jEstdstd-refeh]h]h]uhjh j=ubah}(h]h]h]h]h]refdochj refdomainj=reftyperefrefexplicitrefwarnjW9-2-3-3uhjh!h"hM{h j<ubh//). Data are input using a
keyword-based format:}(h/). Data are input using a
keyword-based format:h j<hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM{h j<hhubjH)}(hLREAD source
id=I typ=T com=’embedded comment’ src=X end
END sourceh]h/LREAD source
id=I typ=T com=’embedded comment’ src=X end
END source}(hhh j1=ubah}(h]h]h]h]h]j=j>uhjGh!h"hMh j<hhubhM)}(hwhereh]h/where}(hjA=h j?=hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh j<hhubjP)}(hhh](hM)}(hI = Source ID number,h]h/I = Source ID number,}(hjR=h jP=ubah}(h]h]h]h]h]uhhLh!h"hMh jM=ubhM)}(hT = Source type,h]h/T = Source type,}(hj`=h j^=ubah}(h]h]h]h]h]uhhLh!h"hMh jM=ubhM)}(h8X = List of source strength values, according to type T.h]h/8X = List of source strength values, according to type T.}(hjn=h jl=ubah}(h]h]h]h]h]uhhLh!h"hMh jM=ubeh}(h]h]h]h]h]uhjOh j<hhh!h"hNubhM)}(hXUp to 80 characters of text may be entered after *com=*, delimited by
single quotes ('). The comment string is optional—the remaining
parameters are required. Currently, only two source types are supported;
the definition of X depends on the source type.h](h/1Up to 80 characters of text may be entered after }(h1Up to 80 characters of text may be entered after h j=hhh!NhNubj)}(h*com=*h]h/com=}(hhh j=ubah}(h]h]h]h]h]uhjh j=ubh/, delimited by
single quotes (‘). The comment string is optional—the remaining
parameters are required. Currently, only two source types are supported;
the definition of X depends on the source type.}(h, delimited by
single quotes ('). The comment string is optional—the remaining
parameters are required. Currently, only two source types are supported;
the definition of X depends on the source type.h j=hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j<hhubhM)}(hoSource type 0 (*typ=0*): A single value of X is supplied—this source
strength is placed in all energy groups.h](h/Source type 0 (}(hSource type 0 (h j=hhh!NhNubj)}(h*typ=0*h]h/typ=0}(hhh j=ubah}(h]h]h]h]h]uhjh j=ubh/Y): A single value of X is supplied—this source
strength is placed in all energy groups.}(hY): A single value of X is supplied—this source
strength is placed in all energy groups.h j=hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j<hhubhM)}(h~Source type 1 (*typ=1*): *G* values of X are supplied, one value for
each energy group. FIDO-type repeat command is supported.h](h/Source type 1 (}(hSource type 1 (h j=hhh!NhNubj)}(h*typ=1*h]h/typ=1}(hhh j=ubah}(h]h]h]h]h]uhjh j=ubh/): }(h): h j=hhh!NhNubj)}(h*G*h]h/G}(hhh j=ubah}(h]h]h]h]h]uhjh j=ubh/b values of X are supplied, one value for
each energy group. FIDO-type repeat command is supported.}(hb values of X are supplied, one value for
each energy group. FIDO-type repeat command is supported.h j=hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j<hhubhM)}(hPAn example of a source specification for two different sources is the
following.h]h/PAn example of a source specification for two different sources is the
following.}(hj=h j=hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh j<hhubjH)}(hREAD source
id=1 typ=1 com=’44-g fuel source’ src=0.44 0.32 0.25 0.01 40r0.0 end
id=5 typ=0 src=0.001 end
END sourceh]h/READ source
id=1 typ=1 com=’44-g fuel source’ src=0.44 0.32 0.25 0.01 40r0.0 end
id=5 typ=0 src=0.001 end
END source}(hhh j>ubah}(h]h]h]h]h]j=j>uhjGh!h"hMh j<hhubhM)}(hXThe Material block is used to associate a given source definition with a
given mixture. The same source may be placed in multiple mixtures. For
generalized adjoint calculations—which require a fixed source derived
for the generalized response of interest (see *Generalized Perturbation
Theory* in the SAMS chapter)—the TRITON control sequence automatically
prepares the NEWT Source block.h](h/XThe Material block is used to associate a given source definition with a
given mixture. The same source may be placed in multiple mixtures. For
generalized adjoint calculations—which require a fixed source derived
for the generalized response of interest (see }(hXThe Material block is used to associate a given source definition with a
given mixture. The same source may be placed in multiple mixtures. For
generalized adjoint calculations—which require a fixed source derived
for the generalized response of interest (see h j>hhh!NhNubj)}(h!*Generalized Perturbation
Theory*h]h/Generalized Perturbation
Theory}(hhh j>ubah}(h]h]h]h]h]uhjh j>ubh/a in the SAMS chapter)—the TRITON control sequence automatically
prepares the NEWT Source block.}(ha in the SAMS chapter)—the TRITON control sequence automatically
prepares the NEWT Source block.h j>hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j<hhubh)}(h.. _9-2-3-5:h]h}(h]h]h]h]h]hid64uhh
hMh j<hhh!h"ubeh}(h](source-blockj<eh]h](source block9-2-3-4eh]h]uhh#h jhhh!h"hMwj}jH>j<sj}j<j<subh$)}(hhh](h))}(hCollapse blockh]h/Collapse block}(hjR>h jP>hhh!NhNubah}(h]h]h]h]h]uhh(h jM>hhh!h"hMubhM)}(h+**Collapse block keyword = coll, collapse**h]h)}(hj`>h]h/'Collapse block keyword = coll, collapse}(hhh jb>ubah}(h]h]h]h]h]uhhh j^>ubah}(h]h]h]h]h]uhhLh!h"hMh jM>hhubhM)}(hXThe Collapse block contains the broad (collapsed) group assignment for
each energy group in the original input group structure. Broad group
assignments must be contiguous. A FIDO-type repeat factor is allowed.
For example, given that a calculation is performed using a
44-energy-group library, in which it is desired to collapse the first
9 groups into a single group, the second 17 groups into a second broad
group, and the remaining 18 groups into a third group, either of the
following could be used.h]h/XThe Collapse block contains the broad (collapsed) group assignment for
each energy group in the original input group structure. Broad group
assignments must be contiguous. A FIDO-type repeat factor is allowed.
For example, given that a calculation is performed using a
44-energy-group library, in which it is desired to collapse the first
9 groups into a single group, the second 17 groups into a second broad
group, and the remaining 18 groups into a third group, either of the
following could be used.}(hjw>h ju>hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jM>hhubjH)}(hread collapse
1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
end collapse
read coll 9r1 17r2 18r3 end collh]h/read collapse
1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
end collapse
read coll 9r1 17r2 18r3 end coll}(hhh j>ubah}(h]h]h]h]h]j=j>uhjGh!h"hMh jM>hhubhM)}(hXIf a collapsing operation is requested, then upon the completion of the
transport iteration, NEWT performs a collapsing operation on all
cross sections for all mixtures in the problem. Cross sections are flux
weighted using the average flux in the mixture in which each nuclide
resides and saved in an AMPX working-format library at the unit
specified by the *wtdlib=* parameter (default=30). Collapsed, or “broad
group,” cross sections may also be printed by setting the parameter
*prtbroad=yes* (default=no). Note that the energy boundaries of the
collapsed cross section are always a subset of the boundaries of the
parent library. Cross sections may not be collapsed to arbitrary energy
boundaries.h](h/XiIf a collapsing operation is requested, then upon the completion of the
transport iteration, NEWT performs a collapsing operation on all
cross sections for all mixtures in the problem. Cross sections are flux
weighted using the average flux in the mixture in which each nuclide
resides and saved in an AMPX working-format library at the unit
specified by the }(hXiIf a collapsing operation is requested, then upon the completion of the
transport iteration, NEWT performs a collapsing operation on all
cross sections for all mixtures in the problem. Cross sections are flux
weighted using the average flux in the mixture in which each nuclide
resides and saved in an AMPX working-format library at the unit
specified by the h j>hhh!NhNubj)}(h *wtdlib=*h]h/wtdlib=}(hhh j>ubah}(h]h]h]h]h]uhjh j>ubh/w parameter (default=30). Collapsed, or “broad
group,” cross sections may also be printed by setting the parameter
}(hw parameter (default=30). Collapsed, or “broad
group,” cross sections may also be printed by setting the parameter
h j>hhh!NhNubj)}(h*prtbroad=yes*h]h/prtbroad=yes}(hhh j>ubah}(h]h]h]h]h]uhjh j>ubh/ (default=no). Note that the energy boundaries of the
collapsed cross section are always a subset of the boundaries of the
parent library. Cross sections may not be collapsed to arbitrary energy
boundaries.}(h (default=no). Note that the energy boundaries of the
collapsed cross section are always a subset of the boundaries of the
parent library. Cross sections may not be collapsed to arbitrary energy
boundaries.h j>hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jM>hhubh)}(h.. _9-2-3-6:h]h}(h]h]h]h]h]hid65uhh
hMh jM>hhh!h"ubeh}(h](collapse-blockjA>eh]h](collapse block9-2-3-5eh]h]uhh#h jhhh!h"hMj}j>j7>sj}jA>j7>subh$)}(hhh](h))}(hGeometry blockh]h/Geometry block}(hj>h j>hhh!NhNubah}(h]h]h]h]h]uhh(h j>hhh!h"hMubhM)}(h+**Geometry block keyword = geom, geometry**h]h)}(hj>h]h/'Geometry block keyword = geom, geometry}(hhh j>ubah}(h]h]h]h]h]uhhh j>ubah}(h]h]h]h]h]uhhLh!h"hMh j>hhubhM)}(hXThe Geometry block is always required. This data block contains
geometric descriptions for all bodies included in the model. NEWT
geometry input is performed based on the SCALE Generalized Geometry
Package (SGGP) paradigm employed in the KENO-VI Monte Carlo code within
SCALE. Those familiar with SGGP as applied in KENO-VI will find the new
format very familiar; however, they will quickly realize that the NEWT
geometry package contrasts most sharply with the 3-D implementation in
KENO‑VI because NEWT is a 2-D code. Hence, third dimension (z-axis)
specifications are omitted, along with other inherently 3-D bodies
supported by KENO-VI. Two other more subtle differences are seen:
(1) users must specify the underlying grid structure associated with
each *unit*, and (2) curved surfaces (e.g., cylinders) are approximated
as N-sided polygons, with user control. Details on these differences are
described in the following subsections and illustrated in examples.h](h/XThe Geometry block is always required. This data block contains
geometric descriptions for all bodies included in the model. NEWT
geometry input is performed based on the SCALE Generalized Geometry
Package (SGGP) paradigm employed in the KENO-VI Monte Carlo code within
SCALE. Those familiar with SGGP as applied in KENO-VI will find the new
format very familiar; however, they will quickly realize that the NEWT
geometry package contrasts most sharply with the 3-D implementation in
KENO‑VI because NEWT is a 2-D code. Hence, third dimension (z-axis)
specifications are omitted, along with other inherently 3-D bodies
supported by KENO-VI. Two other more subtle differences are seen:
(1) users must specify the underlying grid structure associated with
each }(hXThe Geometry block is always required. This data block contains
geometric descriptions for all bodies included in the model. NEWT
geometry input is performed based on the SCALE Generalized Geometry
Package (SGGP) paradigm employed in the KENO-VI Monte Carlo code within
SCALE. Those familiar with SGGP as applied in KENO-VI will find the new
format very familiar; however, they will quickly realize that the NEWT
geometry package contrasts most sharply with the 3-D implementation in
KENO‑VI because NEWT is a 2-D code. Hence, third dimension (z-axis)
specifications are omitted, along with other inherently 3-D bodies
supported by KENO-VI. Two other more subtle differences are seen:
(1) users must specify the underlying grid structure associated with
each h j?hhh!NhNubj)}(h*unit*h]h/unit}(hhh j
?ubah}(h]h]h]h]h]uhjh j?ubh/, and (2) curved surfaces (e.g., cylinders) are approximated
as N-sided polygons, with user control. Details on these differences are
described in the following subsections and illustrated in examples.}(h, and (2) curved surfaces (e.g., cylinders) are approximated
as N-sided polygons, with user control. Details on these differences are
described in the following subsections and illustrated in examples.h j?hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j>hhubhM)}(hXThe SGGP approach for model development is combinatorial in nature.
Hence, intersections are allowed, and the user is given enormous
flexibility to specify, translate, rotate, and combine bodies to create
complex configurations. However, the novice user must first focus on the
basics of model development, as outlined in this subsection. Sample
inputs are provided in :ref:`9-2-4` to demonstrate the development of
more complicated models.h](h/XqThe SGGP approach for model development is combinatorial in nature.
Hence, intersections are allowed, and the user is given enormous
flexibility to specify, translate, rotate, and combine bodies to create
complex configurations. However, the novice user must first focus on the
basics of model development, as outlined in this subsection. Sample
inputs are provided in }(hXqThe SGGP approach for model development is combinatorial in nature.
Hence, intersections are allowed, and the user is given enormous
flexibility to specify, translate, rotate, and combine bodies to create
complex configurations. However, the novice user must first focus on the
basics of model development, as outlined in this subsection. Sample
inputs are provided in h j&?hhh!NhNubj)}(h:ref:`9-2-4`h]j)}(hj1?h]h/9-2-4}(hhh j3?ubah}(h]h](jEstdstd-refeh]h]h]uhjh j/?ubah}(h]h]h]h]h]refdochj refdomainj=?reftyperefrefexplicitrefwarnjW9-2-4uhjh!h"hMh j&?ubh/; to demonstrate the development of
more complicated models.V}(h; to demonstrate the development of
more complicated models.h j&?hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j>hhubhM)}(hX"Geometric arrangements in NEWT are based on a fundamental building block
called a unit. Different units can be arranged in an array. :numref:`fig9-2-7`
illustrates a simple unit and an array of such units. Arrays of units
can be contained inside larger units, and in principle, any level of
nesting can be achieved. Within a unit, various shapes can be specified,
each representing some geometrically distinct medium. In every geometry
specification, a single global unit, which forms the outer boundary for
the entire problem, must be specified.h](h/Geometric arrangements in NEWT are based on a fundamental building block
called a unit. Different units can be arranged in an array. }(hGeometric arrangements in NEWT are based on a fundamental building block
called a unit. Different units can be arranged in an array. h jZ?hhh!NhNubj)}(h:numref:`fig9-2-7`h]jM)}(hje?h]h/fig9-2-7}(hhh jg?ubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jc?ubah}(h]h]h]h]h]refdochj refdomainjq?reftypenumrefrefexplicitrefwarnjWfig9-2-7uhjh!h"hMh jZ?ubh/X
illustrates a simple unit and an array of such units. Arrays of units
can be contained inside larger units, and in principle, any level of
nesting can be achieved. Within a unit, various shapes can be specified,
each representing some geometrically distinct medium. In every geometry
specification, a single global unit, which forms the outer boundary for
the entire problem, must be specified.}(hX
illustrates a simple unit and an array of such units. Arrays of units
can be contained inside larger units, and in principle, any level of
nesting can be achieved. Within a unit, various shapes can be specified,
each representing some geometrically distinct medium. In every geometry
specification, a single global unit, which forms the outer boundary for
the entire problem, must be specified.h jZ?hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j>hhubhM)}(hXhNote that in the models pictured in :numref:`fig9-2-7`, bodies are laid within
a Cartesian grid. This is a hallmark of any NEWT model—the body
specifications combined with an underlying grid structure are used to
define a computational grid in which the NEWT ESC solution algorithm is
applied. :numref:`fig9-2-8` illustrates the grid structure associated with the
array example above. The model consists of a set of arbitrary polygons
used to spatially discretize the bodies of interest. The underlying
Cartesian mesh may be specified for any unit; a Cartesian mesh **must**
be specified for the global unit. The mesh for the global unit is the
primary mesh for the entire problem and is often referred to as the base
grid, whereas the mesh for constituent units within the global unit
constitutes localized refinement and may be referred to as the local, or
unit, grid.h](h/$Note that in the models pictured in }(h$Note that in the models pictured in h j?hhh!NhNubj)}(h:numref:`fig9-2-7`h]jM)}(hj?h]h/fig9-2-7}(hhh j?ubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh j?ubah}(h]h]h]h]h]refdochj refdomainj?reftypenumrefrefexplicitrefwarnjWfig9-2-7uhjh!h"hMh j?ubh/, bodies are laid within
a Cartesian grid. This is a hallmark of any NEWT model—the body
specifications combined with an underlying grid structure are used to
define a computational grid in which the NEWT ESC solution algorithm is
applied. }(h, bodies are laid within
a Cartesian grid. This is a hallmark of any NEWT model—the body
specifications combined with an underlying grid structure are used to
define a computational grid in which the NEWT ESC solution algorithm is
applied. h j?hhh!NhNubj)}(h:numref:`fig9-2-8`h]jM)}(hj?h]h/fig9-2-8}(hhh j?ubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh j?ubah}(h]h]h]h]h]refdochj refdomainj?reftypenumrefrefexplicitrefwarnjWfig9-2-8uhjh!h"hMh j?ubh/ illustrates the grid structure associated with the
array example above. The model consists of a set of arbitrary polygons
used to spatially discretize the bodies of interest. The underlying
Cartesian mesh may be specified for any unit; a Cartesian mesh }(h illustrates the grid structure associated with the
array example above. The model consists of a set of arbitrary polygons
used to spatially discretize the bodies of interest. The underlying
Cartesian mesh may be specified for any unit; a Cartesian mesh h j?hhh!NhNubh)}(h**must**h]h/must}(hhh j?ubah}(h]h]h]h]h]uhhh j?ubh/X(
be specified for the global unit. The mesh for the global unit is the
primary mesh for the entire problem and is often referred to as the base
grid, whereas the mesh for constituent units within the global unit
constitutes localized refinement and may be referred to as the local, or
unit, grid.}(hX(
be specified for the global unit. The mesh for the global unit is the
primary mesh for the entire problem and is often referred to as the base
grid, whereas the mesh for constituent units within the global unit
constitutes localized refinement and may be referred to as the local, or
unit, grid.h j?hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j>hhubhM)}(hXThe NEWT geometry block consists of specifications for a set of basic
building blocks known as units. A *unit* is defined as a collection of
shapes, one of which must be defined as the unit boundary. A complete
unit specification consists of a header and three distinct components:h](h/hThe NEWT geometry block consists of specifications for a set of basic
building blocks known as units. A }(hhThe NEWT geometry block consists of specifications for a set of basic
building blocks known as units. A h j?hhh!NhNubj)}(h*unit*h]h/unit}(hhh j@ubah}(h]h]h]h]h]uhjh j?ubh/ is defined as a collection of
shapes, one of which must be defined as the unit boundary. A complete
unit specification consists of a header and three distinct components:}(h is defined as a collection of
shapes, one of which must be defined as the unit boundary. A complete
unit specification consists of a header and three distinct components:h j?hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j>hhubh;)}(hhh](h@)}(hW**Bodies:** shapes, holes, or array placements that define the bodies
within the unit;
h]hM)}(hV**Bodies:** shapes, holes, or array placements that define the bodies
within the unit;h](h)}(h**Bodies:**h]h/Bodies:}(hhh j'@ubah}(h]h]h]h]h]uhhh j#@ubh/K shapes, holes, or array placements that define the bodies
within the unit;}(hK shapes, holes, or array placements that define the bodies
within the unit;h j#@ubeh}(h]h]h]h]h]uhhLh!h"hM h j@ubah}(h]h]h]h]h]uhh?h j@hhh!h"hNubh@)}(hc**Media** specifications that define the material content
(composition) of the various shapes; and
h]hM)}(hb**Media** specifications that define the material content
(composition) of the various shapes; andh](h)}(h **Media**h]h/Media}(hhh jN@ubah}(h]h]h]h]h]uhhh jJ@ubh/Y specifications that define the material content
(composition) of the various shapes; and}(hY specifications that define the material content
(composition) of the various shapes; andh jJ@ubeh}(h]h]h]h]h]uhhLh!h"hMh jF@ubah}(h]h]h]h]h]uhh?h j@hhh!h"hNubh@)}(h_**Boundary** definition that defines the extent of the unit and its
associated grid structure.
h]hM)}(h^**Boundary** definition that defines the extent of the unit and its
associated grid structure.h](h)}(h**Boundary**h]h/Boundary}(hhh ju@ubah}(h]h]h]h]h]uhhh jq@ubh/R definition that defines the extent of the unit and its
associated grid structure.}(hR definition that defines the extent of the unit and its
associated grid structure.h jq@ubeh}(h]h]h]h]h]uhhLh!h"hMh jm@ubah}(h]h]h]h]h]uhh?h j@hhh!h"hNubeh}(h]h]h]h]h]h~j hhhhuhh:h j>hhh!h"hM ubj)}(h?.. image:: figs/NEWT/fig7-1.png
:align: center
:width: 500
h]h}(h]h]h]h]h]aligncenterwidth500urifigs/NEWT/fig7-1.pngj*}j,j@suhjh j>hhh!h"hNubh)}(h
.. _fig9-2-7:h]h}(h]h]h]h]h]hfig9-2-7uhh
hMh j>hhh!h"ubj)}(hhh](j)}(hx.. figure:: figs/NEWT/fig7-2.png
:align: center
:width: 500
A simple unit (top) and an array of units (bottom).
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig7-2.pngj*}j,j@suhjh j@h!h"hMubj.)}(h3A simple unit (top) and an array of units (bottom).h]h/3A simple unit (top) and an array of units (bottom).}(hj@h j@ubah}(h]h]h]h]h]uhj-h!h"hMh j@ubeh}(h](id165j@eh]h]fig9-2-7ah]h]jEcenteruhjhMh j>hhh!h"j}j@j@sj}j@j@subh)}(h
.. _fig9-2-8:h]h}(h]h]h]h]h]hfig9-2-8uhh
hMh j>hhh!h"ubj)}(hhh](j)}(ho.. figure:: figs/NEWT/fig8.png
:align: center
:width: 500
Computational grid structure in a NEWT model.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig8.pngj*}j,j@suhjh j@h!h"hM#ubj.)}(h-Computational grid structure in a NEWT model.h]h/-Computational grid structure in a NEWT model.}(hjAh j@ubah}(h]h]h]h]h]uhj-h!h"hM#h j@ubeh}(h](id166j@eh]h]fig9-2-8ah]h]jEcenteruhjhM#h j>hhh!h"j}jAj@sj}j@j@subhM)}(hEvery unit begins with a header consisting of the keyword *unit*
followed by a unique integer label (*unit_id)* that serves to identify
the unit:h](h/:Every unit begins with a header consisting of the keyword }(h:Every unit begins with a header consisting of the keyword h jAhhh!NhNubj)}(h*unit*h]h/unit}(hhh j Aubah}(h]h]h]h]h]uhjh jAubh/%
followed by a unique integer label (}(h%
followed by a unique integer label (h jAhhh!NhNubj)}(h
*unit_id)*h]h/unit_id)}(hhh j3Aubah}(h]h]h]h]h]uhjh jAubh/" that serves to identify
the unit:}(h" that serves to identify
the unit:h jAhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM%h j>hhubjH)}(hunit unit_idh]h/unit unit_id}(hhh jLAubah}(h]h]h]h]h]j=j>uhjGh!h"hM+h j>hhubhM)}(hXThe header is followed by a complete unit description consisting of the
three components described above; each of these components of the unit
specification is described in the following subsections. In every NEWT
model, one unit must be defined as the *global unit*. This unit defines
the global coordinate system for the entire problem, and all other units
(if any) must fit within the global unit. Specification of the global
unit is accomplished simply with the format:h](h/The header is followed by a complete unit description consisting of the
three components described above; each of these components of the unit
specification is described in the following subsections. In every NEWT
model, one unit must be defined as the }(hThe header is followed by a complete unit description consisting of the
three components described above; each of these components of the unit
specification is described in the following subsections. In every NEWT
model, one unit must be defined as the h jZAhhh!NhNubj)}(h
*global unit*h]h/global unit}(hhh jcAubah}(h]h]h]h]h]uhjh jZAubh/. This unit defines
the global coordinate system for the entire problem, and all other units
(if any) must fit within the global unit. Specification of the global
unit is accomplished simply with the format:}(h. This unit defines
the global coordinate system for the entire problem, and all other units
(if any) must fit within the global unit. Specification of the global
unit is accomplished simply with the format:h jZAhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM-h j>hhubjH)}(hglobal unit unit_idh]h/global unit unit_id}(hhh j|Aubah}(h]h]h]h]h]j=j>uhjGh!h"hM7h j>hhubhM)}(hThe global unit may occur anywhere in the list of units. If only one
unit is defined in an input, it must be identified as the global unit.h]h/The global unit may occur anywhere in the list of units. If only one
unit is defined in an input, it must be identified as the global unit.}(hjAh jAhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM9h j>hhubhM)}(hAs indicated earlier, the geometry block consists of a list of one or
more units. Each unit is terminated by the beginning of another unit or
by the end of the geometry block. Conceptually, a geometry block will
have the following structure:h]h/As indicated earlier, the geometry block consists of a list of one or
more units. Each unit is terminated by the beginning of another unit or
by the end of the geometry block. Conceptually, a geometry block will
have the following structure:}(hjAh jAhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM<h j>hhubjH)}(hread geom
global unit 1
(unit specifications)
unit 2
(unit specifications)
unit 3
(unit specifications)
…
unit 10
(unit specifications)
end geomh]h/read geom
global unit 1
(unit specifications)
unit 2
(unit specifications)
unit 3
(unit specifications)
…
unit 10
(unit specifications)
end geom}(hhh jAubah}(h]h]h]h]h]j=j>uhjGh!h"hMCh j>hhubhM)}(huThe unit numbers are arbitrary and can occur in any order, although they
must be unique; they serve simply as labels.h]h/uThe unit numbers are arbitrary and can occur in any order, although they
must be unique; they serve simply as labels.}(hjAh jAhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMOh j>hhubhM)}(hHThe remainder of this section describes the various components of units.h]h/HThe remainder of this section describes the various components of units.}(hjAh jAhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMRh j>hhubh)}(h.. _9-2-3-6-1:h]h}(h]h]h]h]h]hid66uhh
hMTh j>hhh!h"ubh$)}(hhh](h))}(hBodiesh]h/Bodies}(hjAh jAhhh!NhNubah}(h]h]h]h]h]uhh(h jAhhh!h"hMWubhM)}(hX/Every unit contains a set of body specifications in terms of (1) basic
*shapes* that are placed directly within a unit; (2) one or more arrays,
each of which is defined elsewhere and placed within a unit with an
*array placement* operator; and (3) holes. Units **must** contain at
least one *shape* specification, which is used to define the spatial
boundaries of the unit. Additional shape specifications may be used as
needed. Holes and/or array placements are optional; there is no
theoretical limit on the number of each that may be used within a unit.h](h/HEvery unit contains a set of body specifications in terms of (1) basic
}(hHEvery unit contains a set of body specifications in terms of (1) basic
h jAhhh!NhNubj)}(h*shapes*h]h/shapes}(hhh jAubah}(h]h]h]h]h]uhjh jAubh/ that are placed directly within a unit; (2) one or more arrays,
each of which is defined elsewhere and placed within a unit with an
}(h that are placed directly within a unit; (2) one or more arrays,
each of which is defined elsewhere and placed within a unit with an
h jAhhh!NhNubj)}(h*array placement*h]h/array placement}(hhh jBubah}(h]h]h]h]h]uhjh jAubh/! operator; and (3) holes. Units }(h! operator; and (3) holes. Units h jAhhh!NhNubh)}(h**must**h]h/must}(hhh jBubah}(h]h]h]h]h]uhhh jAubh/ contain at
least one }(h contain at
least one h jAhhh!NhNubj)}(h*shape*h]h/shape}(hhh j.Bubah}(h]h]h]h]h]uhjh jAubh/X specification, which is used to define the spatial
boundaries of the unit. Additional shape specifications may be used as
needed. Holes and/or array placements are optional; there is no
theoretical limit on the number of each that may be used within a unit.}(hX specification, which is used to define the spatial
boundaries of the unit. Additional shape specifications may be used as
needed. Holes and/or array placements are optional; there is no
theoretical limit on the number of each that may be used within a unit.h jAhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMYh jAhhubh)}(h.. _9-2-3-6-1-1:h]h}(h]h]h]h]h]hid67uhh
hMbh jAhhh!h"ubh$)}(hhh](h))}(hShapesh]h/Shapes}(hjWBh jUBhhh!NhNubah}(h]h]h]h]h]uhh(h jRBhhh!h"hMeubhM)}(hHShapes are simple predefined bodies. NEWT currently supports six shapes:h]h/HShapes are simple predefined bodies. NEWT currently supports six shapes:}(hjeBh jcBhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMgh jRBhhubjP)}(hhh]h;)}(hhh](h@)}(h
cylinder,
h]hM)}(h cylinder,h]h/ cylinder,}(hj}Bh j{Bubah}(h]h]h]h]h]uhhLh!h"hMih jwBubah}(h]h]h]h]h]uhh?h jtBubh@)}(hcuboid,
h]hM)}(hcuboid,h]h/cuboid,}(hjBh jBubah}(h]h]h]h]h]uhhLh!h"hMkh jBubah}(h]h]h]h]h]uhh?h jtBubh@)}(h
hexprism,
h]hM)}(h hexprism,h]h/ hexprism,}(hjBh jBubah}(h]h]h]h]h]uhhLh!h"hMmh jBubah}(h]h]h]h]h]uhh?h jtBubh@)}(hrhexprism (rotated hexprism),
h]hM)}(hrhexprism (rotated hexprism),h]h/rhexprism (rotated hexprism),}(hjBh jBubah}(h]h]h]h]h]uhhLh!h"hMoh jBubah}(h]h]h]h]h]uhh?h jtBubh@)}(hwedge, and
h]hM)}(h
wedge, andh]h/
wedge, and}(hjBh jBubah}(h]h]h]h]h]uhhLh!h"hMqh jBubah}(h]h]h]h]h]uhh?h jtBubh@)}(h polygon.
h]hM)}(hpolygon.h]h/polygon.}(hjBh jBubah}(h]h]h]h]h]uhhLh!h"hMsh jBubah}(h]h]h]h]h]uhh?h jtBubeh}(h]h]h]h]h]h~j hhhhuhh:h jqBubah}(h]h]h]h]h]uhjOh jRBhhh!NhNubhM)}(hX)The names of these shapes are generally associated with 3-D bodies but
are used in NEWT to be consistent with KENO-VI nomenclature. In NEWT, a
cylinder is equivalent to a circle, a cuboid is equivalent to a
rectangle, a hexprism is equivalent to a hexagon, and a wedge is
equivalent to a triangle.h]h/X)The names of these shapes are generally associated with 3-D bodies but
are used in NEWT to be consistent with KENO-VI nomenclature. In NEWT, a
cylinder is equivalent to a circle, a cuboid is equivalent to a
rectangle, a hexprism is equivalent to a hexagon, and a wedge is
equivalent to a triangle.}(hjCh jChhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMuh jRBhhubhM)}(hXBecause the SGGP is combinatorial in nature, intersection and overlap of
shapes is permitted. For this reason, no specific mixture is associated
with each shape. Combinatorial logic allows a fraction of a shape to be
filled with one mixture, while the remainder or another fraction thereof
may be assigned a different mixture. This is discussed further in the
section **Media Specifications** in the description of *media*
assignment (:ref:`9-2-3-6-2`).h](h/XpBecause the SGGP is combinatorial in nature, intersection and overlap of
shapes is permitted. For this reason, no specific mixture is associated
with each shape. Combinatorial logic allows a fraction of a shape to be
filled with one mixture, while the remainder or another fraction thereof
may be assigned a different mixture. This is discussed further in the
section }(hXpBecause the SGGP is combinatorial in nature, intersection and overlap of
shapes is permitted. For this reason, no specific mixture is associated
with each shape. Combinatorial logic allows a fraction of a shape to be
filled with one mixture, while the remainder or another fraction thereof
may be assigned a different mixture. This is discussed further in the
section h j!Chhh!NhNubh)}(h**Media Specifications**h]h/Media Specifications}(hhh j*Cubah}(h]h]h]h]h]uhhh j!Cubh/ in the description of }(h in the description of h j!Chhh!NhNubj)}(h*media*h]h/media}(hhh j=Cubah}(h]h]h]h]h]uhjh j!Cubh/
assignment (}(h
assignment (h j!Chhh!NhNubj)}(h:ref:`9-2-3-6-2`h]j)}(hjRCh]h/ 9-2-3-6-2}(hhh jTCubah}(h]h](jEstdstd-refeh]h]h]uhjh jPCubah}(h]h]h]h]h]refdochj refdomainj^CreftyperefrefexplicitrefwarnjW 9-2-3-6-2uhjh!h"hM{h j!Cubh/).}(h).h j!Chhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM{h jRBhhubhM)}(hEach shape is specified by name, an associated body identification
(*body_id*) number, and dimensioning data. The *body_id* number is
arbitrary but must be unique within each unit. Specific formats for each
shape are provided below.h](h/DEach shape is specified by name, an associated body identification
(}(hDEach shape is specified by name, an associated body identification
(h j{Chhh!NhNubj)}(h *body_id*h]h/body_id}(hhh jCubah}(h]h]h]h]h]uhjh j{Cubh/%) number, and dimensioning data. The }(h%) number, and dimensioning data. The h j{Chhh!NhNubj)}(h *body_id*h]h/body_id}(hhh jCubah}(h]h]h]h]h]uhjh j{Cubh/m number is
arbitrary but must be unique within each unit. Specific formats for each
shape are provided below.}(hm number is
arbitrary but must be unique within each unit. Specific formats for each
shape are provided below.h j{Chhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jRBhhubh)}(h.. _9-2-3-6-1-2:h]h}(h]h]h]h]h]hid68uhh
hMh jRBhhh!h"ubeh}(h](shapesjQBeh]h](shapes9-2-3-6-1-1eh]h]uhh#h jAhhh!h"hMej}jCjGBsj}jQBjGBsubh$)}(hhh](h))}(hCylinderh]h/Cylinder}(hjCh jChhh!NhNubah}(h]h]h]h]h]uhh(h jChhh!h"hMubhM)}(hCylinderh]h/Cylinder}(hjCh jChhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jChhubhM)}(h4The cylinder specification has the following format:h]h/4The cylinder specification has the following format:}(hjCh jChhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jChhubjH)}(h*cylinder body_id radius [modifier_list]h]h/*cylinder body_id radius [modifier_list]}(hhh jCubah}(h]h]h]h]h]j=j>uhjGh!h"hMh jChhubhM)}(hX]where radius is the radius of the circle. The circle will be centered at
(0,0). The modifier list is an optional set of operations that may be
performed on each shape. One of the modifiers allowed is the *origin*
modifier, which lets one translate the origin of a shape to a different
location. Modifier commands are described later in this section.h](h/where radius is the radius of the circle. The circle will be centered at
(0,0). The modifier list is an optional set of operations that may be
performed on each shape. One of the modifiers allowed is the }(hwhere radius is the radius of the circle. The circle will be centered at
(0,0). The modifier list is an optional set of operations that may be
performed on each shape. One of the modifiers allowed is the h jDhhh!NhNubj)}(h*origin*h]h/origin}(hhh j
Dubah}(h]h]h]h]h]uhjh jDubh/
modifier, which lets one translate the origin of a shape to a different
location. Modifier commands are described later in this section.}(h
modifier, which lets one translate the origin of a shape to a different
location. Modifier commands are described later in this section.h jDhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jChhubh)}(h.. _9-2-3-6-1-3:h]h}(h]h]h]h]h]hid69uhh
hMh jChhh!h"ubeh}(h](cylinderjCeh]h](cylinder9-2-3-6-1-2eh]h]uhh#h jAhhh!h"hMj}j4DjCsj}jCjCsubh$)}(hhh](h))}(hCuboidh]h/Cuboid}(hj>Dh juhjGh!h"hMh j9DhhubhM)}(hXwhere (x\ :sub:`min`, y\ :sub:`min`) and (x\ :sub:`max`, y\ :sub:`max`)
represent the lower-left and upper-right vertices of a rectangle on a
Cartesian coordinate system. Note that the cuboid is explicitly placed
by its coordinates; no translation is required (or allowed).h](h/
where (x }(h
where (x\ h jfDhhh!NhNubj)}(h
:sub:`min`h]h/min}(hhh joDubah}(h]h]h]h]h]uhjh jfDubh/, y }(h, y\ h jfDhhh!NhNubj)}(h
:sub:`min`h]h/min}(hhh jDubah}(h]h]h]h]h]uhjh jfDubh/
) and (x }(h
) and (x\ h jfDhhh!NhNubj)}(h
:sub:`max`h]h/max}(hhh jDubah}(h]h]h]h]h]uhjh jfDubh/, y }(hjDh jfDubj)}(h
:sub:`max`h]h/max}(hhh jDubah}(h]h]h]h]h]uhjh jfDubh/)
represent the lower-left and upper-right vertices of a rectangle on a
Cartesian coordinate system. Note that the cuboid is explicitly placed
by its coordinates; no translation is required (or allowed).}(h)
represent the lower-left and upper-right vertices of a rectangle on a
Cartesian coordinate system. Note that the cuboid is explicitly placed
by its coordinates; no translation is required (or allowed).h jfDhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j9Dhhubh)}(h.. _9-2-3-6-1-4:h]h}(h]h]h]h]h]hid70uhh
hMh j9Dhhh!h"ubeh}(h](cuboidj-Deh]h](cuboid9-2-3-6-1-3eh]h]uhh#h jAhhh!h"hMj}jDj#Dsj}j-Dj#Dsubh$)}(hhh](h))}(hHexprism and rhexprismh]h/Hexprism and rhexprism}(hjDh jDhhh!NhNubah}(h]h]h]h]h]uhh(h jDhhh!h"hMubhM)}(hIBoth hexprisms are specified in a manner identical to that of a
cylinder:h]h/IBoth hexprisms are specified in a manner identical to that of a
cylinder:}(hjDh jDhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jDhhubjH)}(hUhexprism body_id radius [modifier_list]
rhexprism body_id radius [modifier_list]h]h/Uhexprism body_id radius [modifier_list]
rhexprism body_id radius [modifier_list]}(hhh jDubah}(h]h]h]h]h]j=j>uhjGh!h"hMh jDhhubhM)}(hXwhere *radius* is the inner/minor radius of the hexagon. A standard
hexagon (*hexprism)* is oriented with vertices at the top and bottom, as
illustrated in :numref:`fig9-2-9`. A rotated hexagon (*rhexprism*) is oriented
with vertices on the left and right sides, as illustrated in
:numref:`fig9-2-10`. Both types of hexprisms, like cylinders, are by default
placed with their origins at (0,0). However, like cylinders, they can
also be translated in space via the *origin* translation command.h](h/where }(hwhere h jEhhh!NhNubj)}(h*radius*h]h/radius}(hhh jEubah}(h]h]h]h]h]uhjh jEubh/? is the inner/minor radius of the hexagon. A standard
hexagon (}(h? is the inner/minor radius of the hexagon. A standard
hexagon (h jEhhh!NhNubj)}(h*hexprism)*h]h/ hexprism)}(hhh jEubah}(h]h]h]h]h]uhjh jEubh/D is oriented with vertices at the top and bottom, as
illustrated in }(hD is oriented with vertices at the top and bottom, as
illustrated in h jEhhh!NhNubj)}(h:numref:`fig9-2-9`h]jM)}(hj4Eh]h/fig9-2-9}(hhh j6Eubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh j2Eubah}(h]h]h]h]h]refdochj refdomainj@EreftypenumrefrefexplicitrefwarnjWfig9-2-9uhjh!h"hMh jEubh/. A rotated hexagon (}(h. A rotated hexagon (h jEhhh!NhNubj)}(h*rhexprism*h]h/ rhexprism}(hhh jWEubah}(h]h]h]h]h]uhjh jEubh/K) is oriented
with vertices on the left and right sides, as illustrated in
}(hK) is oriented
with vertices on the left and right sides, as illustrated in
h jEhhh!NhNubj)}(h:numref:`fig9-2-10`h]jM)}(hjlEh]h/ fig9-2-10}(hhh jnEubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jjEubah}(h]h]h]h]h]refdochj refdomainjxEreftypenumrefrefexplicitrefwarnjW fig9-2-10uhjh!h"hMh jEubh/. Both types of hexprisms, like cylinders, are by default
placed with their origins at (0,0). However, like cylinders, they can
also be translated in space via the }(h. Both types of hexprisms, like cylinders, are by default
placed with their origins at (0,0). However, like cylinders, they can
also be translated in space via the h jEhhh!NhNubj)}(h*origin*h]h/origin}(hhh jEubah}(h]h]h]h]h]uhjh jEubh/ translation command.}(h translation command.h jEhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jDhhubh)}(h
.. _fig9-2-9:h]h}(h]h]h]h]h]hfig9-2-9uhh
hMh jDhhh!h"ubj)}(hhh](j)}(he.. figure:: figs/NEWT/fig9.png
:align: center
:width: 400
Orientation of a standard hexprism.
h]h}(h]h]h]h]h]width400urifigs/NEWT/fig9.pngj*}j,jEsuhjh jEh!h"hMubj.)}(h#Orientation of a standard hexprism.h]h/#Orientation of a standard hexprism.}(hjEh jEubah}(h]h]h]h]h]uhj-h!h"hMh jEubeh}(h](id167jEeh]h]fig9-2-9ah]h]jEcenteruhjhMh jDhhh!h"j}jEjEsj}jEjEsubh)}(h.. _fig9-2-10:h]h}(h]h]h]h]h]h fig9-2-10uhh
hMh jDhhh!h"ubj)}(hhh](j)}(hf.. figure:: figs/NEWT/fig10.png
:align: center
:width: 400
Orientation of a rotated hexprism.
h]h}(h]h]h]h]h]width400urifigs/NEWT/fig10.pngj*}j,jEsuhjh jEh!h"hMubj.)}(h"Orientation of a rotated hexprism.h]h/"Orientation of a rotated hexprism.}(hjEh jEubah}(h]h]h]h]h]uhj-h!h"hMh jEubeh}(h](id168jEeh]h] fig9-2-10ah]h]jEcenteruhjhMh jDhhh!h"j}jFjEsj}jEjEsubh)}(h.. _9-2-3-6-1-5:h]h}(h]h]h]h]h]hid71uhh
hMh jDhhh!h"ubeh}(h](hexprism-and-rhexprismjDeh]h](hexprism and rhexprism9-2-3-6-1-4eh]h]uhh#h jAhhh!h"hMj}j%FjDsj}jDjDsubh$)}(hhh](h))}(hWedgeh]h/Wedge}(hj/Fh j-Fhhh!NhNubah}(h]h]h]h]h]uhh(h j*Fhhh!h"hMubhM)}(h=A wedge, or triangle, specification has the following format:h]h/=A wedge, or triangle, specification has the following format:}(hj=Fh j;Fhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh j*FhhubjH)}(h-wedge body_id xbase xpt ypt [modifier_list]h]h/-wedge body_id xbase xpt ypt [modifier_list]}(hhh jIFubah}(h]h]h]h]h]j=j>uhjGh!h"hMh j*FhhubhM)}(hXLwhere the vertices of the shape are defined as (0,0), (x\ :sub:`base`,0),
and (x\ :sub:`pt`,y\ :sub:`pt`). Thus, one side always lies on the x-axis.
The modifiers *origin* and *rotate* may be used to position and orient
the triangle in the problem domain. :numref:`fig9-2-11` illustrates placement
of a wedge using these parameters.h](h/:where the vertices of the shape are defined as (0,0), (x }(h:where the vertices of the shape are defined as (0,0), (x\ h jWFhhh!NhNubj)}(h:sub:`base`h]h/base}(hhh j`Fubah}(h]h]h]h]h]uhjh jWFubh/
,0),
and (x }(h
,0),
and (x\ h jWFhhh!NhNubj)}(h :sub:`pt`h]h/pt}(hhh jsFubah}(h]h]h]h]h]uhjh jWFubh/,y }(h,y\ h jWFhhh!NhNubj)}(h :sub:`pt`h]h/pt}(hhh jFubah}(h]h]h]h]h]uhjh jWFubh/;). Thus, one side always lies on the x-axis.
The modifiers }(h;). Thus, one side always lies on the x-axis.
The modifiers h jWFhhh!NhNubj)}(h*origin*h]h/origin}(hhh jFubah}(h]h]h]h]h]uhjh jWFubh/ and }(h and h jWFhhh!NhNubj)}(h*rotate*h]h/rotate}(hhh jFubah}(h]h]h]h]h]uhjh jWFubh/H may be used to position and orient
the triangle in the problem domain. }(hH may be used to position and orient
the triangle in the problem domain. h jWFhhh!NhNubj)}(h:numref:`fig9-2-11`h]jM)}(hjFh]h/ fig9-2-11}(hhh jFubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jFubah}(h]h]h]h]h]refdochj refdomainjFreftypenumrefrefexplicitrefwarnjW fig9-2-11uhjh!h"hMh jWFubh/9 illustrates placement
of a wedge using these parameters.}(h9 illustrates placement
of a wedge using these parameters.h jWFhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j*Fhhubh)}(h.. _fig9-2-11:h]h}(h]h]h]h]h]h fig9-2-11uhh
hMh j*Fhhh!h"ubj)}(hhh](j)}(hi.. figure:: figs/NEWT/fig11.png
:align: center
:width: 400
Initial positioning of the wedge body.
h]h}(h]h]h]h]h]width400urifigs/NEWT/fig11.pngj*}j,jGsuhjh jFh!h"hMubj.)}(h&Initial positioning of the wedge body.h]h/&Initial positioning of the wedge body.}(hj Gh jGubah}(h]h]h]h]h]uhj-h!h"hMh jFubeh}(h](id169jFeh]h] fig9-2-11ah]h]jEcenteruhjhMh j*Fhhh!h"j}jGjFsj}jFjFsubh)}(h.. _9-2-3-6-1-6:h]h}(h]h]h]h]h]hid72uhh
hMh j*Fhhh!h"ubeh}(h](wedgejFeh]h](wedge9-2-3-6-1-5eh]h]uhh#h jAhhh!h"hMj}j1GjFsj}jFjFsubh$)}(hhh](h))}(hPolygonh]h/Polygon}(hj;Gh j9Ghhh!NhNubah}(h]h]h]h]h]uhh(h j6Ghhh!h"hMubhM)}(h3The polygon specification has the following format:h]h/3The polygon specification has the following format:}(hjIGh jGGhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh j6GhhubjH)}(h5polygon body_id x0, y0, x1, y1, ..., xN, yN, x0, y0h]h/5polygon body_id x0, y0, x1, y1, ..., xN, yN, x0, y0}(hhh jUGubah}(h]h]h]h]h]j=j>uhjGh!h"hMh j6GhhubhM)}(hwhere (x\ :sub:`i`, y\ :sub:`i`) are the polygon vertices (the first and
last pair in this list refer to the same vertex). Note that the polygon
is explicitly placed by its coordinates; no translation is required (or
allowed).h](h/
where (x }(h
where (x\ h jcGhhh!NhNubj)}(h:sub:`i`h]h/i}(hhh jlGubah}(h]h]h]h]h]uhjh jcGubh/, y }(h, y\ h jcGhhh!NhNubj)}(h:sub:`i`h]h/i}(hhh jGubah}(h]h]h]h]h]uhjh jcGubh/) are the polygon vertices (the first and
last pair in this list refer to the same vertex). Note that the polygon
is explicitly placed by its coordinates; no translation is required (or
allowed).}(h) are the polygon vertices (the first and
last pair in this list refer to the same vertex). Note that the polygon
is explicitly placed by its coordinates; no translation is required (or
allowed).h jcGhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j6Ghhubh)}(h.. _9-2-3-6-1-7:h]h}(h]h]h]h]h]hid73uhh
hMh j6Ghhh!h"ubeh}(h](polygonj*Geh]h](polygon9-2-3-6-1-6eh]h]uhh#h jAhhh!h"hMj}jGj Gsj}j*Gj Gsubh$)}(hhh](h))}(hExample of shape specificationsh]h/Example of shape specifications}(hjGh jGhhh!NhNubah}(h]h]h]h]h]uhh(h jGhhh!h"hMubhM)}(hUse of shapes within a unit can be illustrated with a simple example.
Consider a unit, arbitrarily labeled with *unit_id*\ =10, containing a
cuboid and two cylinders. Each shape is given a unique (but arbitrary)
*body_id*.h](h/pUse of shapes within a unit can be illustrated with a simple example.
Consider a unit, arbitrarily labeled with }(hpUse of shapes within a unit can be illustrated with a simple example.
Consider a unit, arbitrarily labeled with h jGhhh!NhNubj)}(h *unit_id*h]h/unit_id}(hhh jGubah}(h]h]h]h]h]uhjh jGubh/[ =10, containing a
cuboid and two cylinders. Each shape is given a unique (but arbitrary)
}(h[\ =10, containing a
cuboid and two cylinders. Each shape is given a unique (but arbitrary)
h jGhhh!NhNubj)}(h *body_id*h]h/body_id}(hhh jGubah}(h]h]h]h]h]uhjh jGubh/.}(hhh jGhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jGhhubjH)}(hQunit 10
cuboid 11 3.0 -5.0 1.0 -2.0
cylinder 12 0.8
cylinder 13 0.6h]h/Qunit 10
cuboid 11 3.0 -5.0 1.0 -2.0
cylinder 12 0.8
cylinder 13 0.6}(hhh jGubah}(h]h]h]h]h]j=j>uhjGh!h"hMh jGhhubhM)}(hXThe cuboid is explicitly placed by its coordinates; the two cylinders
will by default be placed at (0,0). Use of the *origin* command to
relocate cylinders is introduced below. :numref:`fig9-2-12` illustrates the
body placement that occurs for the given example.h](h/uThe cuboid is explicitly placed by its coordinates; the two cylinders
will by default be placed at (0,0). Use of the }(huThe cuboid is explicitly placed by its coordinates; the two cylinders
will by default be placed at (0,0). Use of the h jHhhh!NhNubj)}(h*origin*h]h/origin}(hhh j
Hubah}(h]h]h]h]h]uhjh jHubh/4 command to
relocate cylinders is introduced below. }(h4 command to
relocate cylinders is introduced below. h jHhhh!NhNubj)}(h:numref:`fig9-2-12`h]jM)}(hjHh]h/ fig9-2-12}(hhh j!Hubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jHubah}(h]h]h]h]h]refdochj refdomainj+HreftypenumrefrefexplicitrefwarnjW fig9-2-12uhjh!h"hM
h jHubh/B illustrates the
body placement that occurs for the given example.}(hB illustrates the
body placement that occurs for the given example.h jHhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM
h jGhhubh)}(h.. _fig9-2-12:h]h}(h]h]h]h]h]h fig9-2-12uhh
hMh jGhhh!h"ubj)}(hhh](j)}(hr.. figure:: figs/NEWT/fig12.png
:align: center
:width: 400
Body placement for two cylinders and a cuboid.
h]h}(h]h]h]h]h]width400urifigs/NEWT/fig12.pngj*}j,jcHsuhjh jSHh!h"hMubj.)}(h.Body placement for two cylinders and a cuboid.h]h/.Body placement for two cylinders and a cuboid.}(hjgHh jeHubah}(h]h]h]h]h]uhj-h!h"hMh jSHubeh}(h](id170jRHeh]h] fig9-2-12ah]h]jEcenteruhjhMh jGhhh!h"j}jxHjHHsj}jRHjHHsubh)}(h.. _9-2-3-6-1-8:h]h}(h]h]h]h]h]hid74uhh
hMh jGhhh!h"ubeh}(h](example-of-shape-specificationsjGeh]h](example of shape specifications9-2-3-6-1-7eh]h]uhh#h jAhhh!h"hMj}jHjGsj}jGjGsubh$)}(hhh](h))}(hShape modifier commandsh]h/Shape modifier commands}(hjHh jHhhh!NhNubah}(h]h]h]h]h]uhh(h jHhhh!h"hMubhM)}(hModifier commands are provided as a means to perform specific functions
relative to the input shape. The five available modifier commands and
the shapes to which they may be applied are listed here:h]h/Modifier commands are provided as a means to perform specific functions
relative to the input shape. The five available modifier commands and
the shapes to which they may be applied are listed here:}(hjHh jHhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jHhhubjP)}(hhh](hM)}(hM*origin* — translation of center bodies (cylinders, hexprisms,
rhexprisms);h](j)}(h*origin*h]h/origin}(hhh jHubah}(h]h]h]h]h]uhjh jHubh/E — translation of center bodies (cylinders, hexprisms,
rhexprisms);}(hE — translation of center bodies (cylinders, hexprisms,
rhexprisms);h jHubeh}(h]h]h]h]h]uhhLh!h"hM h jHubhM)}(hJ*rotate* — rotation of bodies with respect to the transverse axis
(all);h](j)}(h*rotate*h]h/rotate}(hhh jHubah}(h]h]h]h]h]uhjh jHubh/B — rotation of bodies with respect to the transverse axis
(all);}(hB — rotation of bodies with respect to the transverse axis
(all);h jHubeh}(h]h]h]h]h]uhhLh!h"hM#h jHubhM)}(hl*chord* — removal of a portion of a body with x-plane and y-plane
cuts (cylinders, hexprisms, rhexprisms);h](j)}(h*chord*h]h/chord}(hhh jHubah}(h]h]h]h]h]uhjh jHubh/e — removal of a portion of a body with x-plane and y-plane
cuts (cylinders, hexprisms, rhexprisms);}(he — removal of a portion of a body with x-plane and y-plane
cuts (cylinders, hexprisms, rhexprisms);h jHubeh}(h]h]h]h]h]uhhLh!h"hM&h jHubhM)}(h:*com* — addition of a comment to a specific shape (all);h](j)}(h*com*h]h/com}(hhh jIubah}(h]h]h]h]h]uhjh j
Iubh/5 — addition of a comment to a specific shape (all);}(h5 — addition of a comment to a specific shape (all);h j
Iubeh}(h]h]h]h]h]uhhLh!h"hM)h jHubhM)}(hS*sides* — number of sides used to approximate a circle (cylinder,
default is 12).h](j)}(h*sides*h]h/sides}(hhh j.Iubah}(h]h]h]h]h]uhjh j*Iubh/L — number of sides used to approximate a circle (cylinder,
default is 12).}(hL — number of sides used to approximate a circle (cylinder,
default is 12).h j*Iubeh}(h]h]h]h]h]uhhLh!h"hM+h jHubeh}(h]h]h]h]h]uhjOh jHhhh!h"hNubhM)}(h.The format for each of these commands follows.h]h/.The format for each of these commands follows.}(hjOIh jMIhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM.h jHhhubh)}(h.. _9-2-3-6-1-9:h]h}(h]h]h]h]h]hid75uhh
hM0h jHhhh!h"ubeh}(h](shape-modifier-commandsjHeh]h](shape modifier commands9-2-3-6-1-8eh]h]uhh#h jAhhh!h"hMj}jlIj~Hsj}jHj~Hsubh$)}(hhh](h))}(hORIGINh]h/ORIGIN}(hjvIh jtIhhh!NhNubah}(h]h]h]h]h]uhh(h jqIhhh!h"hM3ubhM)}(hThe *origin* modifier is used to translate the origin of a cylinder or
hexprism from the default origin of (0,0) to some other location. It has
the formath](h/The }(hThe h jIhhh!NhNubj)}(h*origin*h]h/origin}(hhh jIubah}(h]h]h]h]h]uhjh jIubh/ modifier is used to translate the origin of a cylinder or
hexprism from the default origin of (0,0) to some other location. It has
the format}(h modifier is used to translate the origin of a cylinder or
hexprism from the default origin of (0,0) to some other location. It has
the formath jIhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM5h jqIhhubjH)}(horigin x=xnew y=ynewh]h/origin x=xnew y=ynew}(hhh jIubah}(h]h]h]h]h]j=j>uhjGh!h"hM;h jqIhhubhM)}(hwhere (x\ :sub:`new`, y\ :sub:`new`) is the new center of the shape. The
modifier *origin* may not be applied to cuboids, as the location of a
cuboid is explicitly set by its shape specification. If not specified,
each ordinate is set to zero, such thath](h/
where (x }(h
where (x\ h jIhhh!NhNubj)}(h
:sub:`new`h]h/new}(hhh jIubah}(h]h]h]h]h]uhjh jIubh/, y }(h, y\ h jIhhh!NhNubj)}(h
:sub:`new`h]h/new}(hhh jIubah}(h]h]h]h]h]uhjh jIubh//) is the new center of the shape. The
modifier }(h/) is the new center of the shape. The
modifier h jIhhh!NhNubj)}(h*origin*h]h/origin}(hhh jIubah}(h]h]h]h]h]uhjh jIubh/ may not be applied to cuboids, as the location of a
cuboid is explicitly set by its shape specification. If not specified,
each ordinate is set to zero, such that}(h may not be applied to cuboids, as the location of a
cuboid is explicitly set by its shape specification. If not specified,
each ordinate is set to zero, such thath jIhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM=h jqIhhubjH)}(h
origin x=5h]h/
origin x=5}(hhh jIubah}(h]h]h]h]h]j=j>uhjGh!h"hMDh jqIhhubhM)}(his equivalent toh]h/is equivalent to}(hj
Jh jJhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMFh jqIhhubjH)}(horigin x=5 y=0 .h]h/origin x=5 y=0 .}(hhh jJubah}(h]h]h]h]h]j=j>uhjGh!h"hMJh jqIhhubhM)}(hFor example, consider a cuboid whose lower-left and upper-right corners are
located at (0,0) and (1,1), respectively. If one places a cylinder with radius
0.3 in the center of this box [i.e., centered at (0.5, 0.5)], this would be
specified as follows:h]h/For example, consider a cuboid whose lower-left and upper-right corners are
located at (0,0) and (1,1), respectively. If one places a cylinder with radius
0.3 in the center of this box [i.e., centered at (0.5, 0.5)], this would be
specified as follows:}(hj&Jh j$Jhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMLh jqIhhubjH)}(hCunit 1
cuboid 10 1.0 0.0 1.0 0.0
cylinder 20 0.3 origin x=0.5 y=0.5h]h/Cunit 1
cuboid 10 1.0 0.0 1.0 0.0
cylinder 20 0.3 origin x=0.5 y=0.5}(hhh j2Jubah}(h]h]h]h]h]j=j>uhjGh!h"hMSh jqIhhubhM)}(h9This configuration is illustrated in :numref:`fig9-2-13`.h](h/%This configuration is illustrated in }(h%This configuration is illustrated in h j@Jhhh!NhNubj)}(h:numref:`fig9-2-13`h]jM)}(hjKJh]h/ fig9-2-13}(hhh jMJubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jIJubah}(h]h]h]h]h]refdochj refdomainjWJreftypenumrefrefexplicitrefwarnjW fig9-2-13uhjh!h"hMWh j@Jubh/.}(hhh j@Jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMWh jqIhhubh)}(h.. _fig9-2-13:h]h}(h]h]h]h]h]h fig9-2-13uhh
hMYh jqIhhh!h"ubj)}(hhh](j)}(hw.. figure:: figs/NEWT/fig13.png
:align: center
:width: 400
Relocation (translation) of a cylinder using origin.
h]h}(h]h]h]h]h]width400urifigs/NEWT/fig13.pngj*}j,jJsuhjh j~Jh!h"hM^ubj.)}(h4Relocation (translation) of a cylinder using origin.h]h/4Relocation (translation) of a cylinder using origin.}(hjJh jJubah}(h]h]h]h]h]uhj-h!h"hM^h j~Jubeh}(h](id171j}Jeh]h] fig9-2-13ah]h]jEcenteruhjhM^h jqIhhh!h"j}jJjsJsj}j}JjsJsubh)}(h.. _9-2-3-6-1-10:h]h}(h]h]h]h]h]hid76uhh
hM`h jqIhhh!h"ubeh}(h](originjeIeh]h](origin9-2-3-6-1-9eh]h]uhh#h jAhhh!h"hM3j}jJj[Isj}jeIj[Isubh$)}(hhh](h))}(hRotateh]h/Rotate}(hjJh jJhhh!NhNubah}(h]h]h]h]h]uhh(h jJhhh!h"hMcubhM)}(hThe *rotate* body modifier is used to rotate a body around its geometric
center. It can be applied to any body type, but rotation of a cylinder
has no real meaning. The format of the *rotate* modifier is as follows:h](h/The }(hThe h jJhhh!NhNubj)}(h*rotate*h]h/rotate}(hhh jJubah}(h]h]h]h]h]uhjh jJubh/ body modifier is used to rotate a body around its geometric
center. It can be applied to any body type, but rotation of a cylinder
has no real meaning. The format of the }(h body modifier is used to rotate a body around its geometric
center. It can be applied to any body type, but rotation of a cylinder
has no real meaning. The format of the h jJhhh!NhNubj)}(h*rotate*h]h/rotate}(hhh jJubah}(h]h]h]h]h]uhjh jJubh/ modifier is as follows:}(h modifier is as follows:h jJhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMeh jJhhubjH)}(hrotate a1=Ah]h/rotate a1=A}(hhh jKubah}(h]h]h]h]h]j=j>uhjGh!h"hMkh jJhhubhM)}(hXwhere *A* is the angle of rotation, in degrees, in a counterclockwise
direction. All bodies lie in the (x,y) plane, with rotation around the
z-axis, but with respect to the centroid of the body. Rotation always
occurs **before** translation (via *origin*), irrespective of the order
of *rotate* and *origin* commands in the modifier list for a body.
KENO-VI allows rotation about the x and y axes as well, through a2= and
a3=; however, only rotation about the z axis is permitted in NEWT.h](h/where }(hwhere h jKhhh!NhNubj)}(h*A*h]h/A}(hhh jKubah}(h]h]h]h]h]uhjh jKubh/ is the angle of rotation, in degrees, in a counterclockwise
direction. All bodies lie in the (x,y) plane, with rotation around the
z-axis, but with respect to the centroid of the body. Rotation always
occurs }(h is the angle of rotation, in degrees, in a counterclockwise
direction. All bodies lie in the (x,y) plane, with rotation around the
z-axis, but with respect to the centroid of the body. Rotation always
occurs h jKhhh!NhNubh)}(h
**before**h]h/before}(hhh j/Kubah}(h]h]h]h]h]uhhh jKubh/ translation (via }(h translation (via h jKhhh!NhNubj)}(h*origin*h]h/origin}(hhh jBKubah}(h]h]h]h]h]uhjh jKubh/ ), irrespective of the order
of }(h ), irrespective of the order
of h jKhhh!NhNubj)}(h*rotate*h]h/rotate}(hhh jUKubah}(h]h]h]h]h]uhjh jKubh/ and }(h and h jKhhh!NhNubj)}(h*origin*h]h/origin}(hhh jhKubah}(h]h]h]h]h]uhjh jKubh/ commands in the modifier list for a body.
KENO-VI allows rotation about the x and y axes as well, through a2= and
a3=; however, only rotation about the z axis is permitted in NEWT.}(h commands in the modifier list for a body.
KENO-VI allows rotation about the x and y axes as well, through a2= and
a3=; however, only rotation about the z axis is permitted in NEWT.h jKhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMmh jJhhubhM)}(hAs an example, consider a 1 by 1 cm cuboid centered at (0,0), place a
smaller 0.5 by 0.5 cm cuboid inside it, and rotate it 30 degrees
clockwise.h]h/As an example, consider a 1 by 1 cm cuboid centered at (0,0), place a
smaller 0.5 by 0.5 cm cuboid inside it, and rotate it 30 degrees
clockwise.}(hjKh jKhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMuh jJhhubjH)}(hRunit 1
cuboid 10 0.5 -0.5 0.5 -0.5
cuboid 10 0.25 -0.25 0.25 -0.25 rotate a1=-30h]h/Runit 1
cuboid 10 0.5 -0.5 0.5 -0.5
cuboid 10 0.25 -0.25 0.25 -0.25 rotate a1=-30}(hhh jKubah}(h]h]h]h]h]j=j>uhjGh!h"hM{h jJhhubh)}(h.. _fig9-2-14:h]h}(h]h]h]h]h]h fig9-2-14uhh
hMh jJhhh!h"ubj)}(hhh](j)}(hX.. figure:: figs/NEWT/fig14.png
:align: center
:width: 400
Rotation of a cuboid.
h]h}(h]h]h]h]h]width400urifigs/NEWT/fig14.pngj*}j,jKsuhjh jKh!h"hMubj.)}(hRotation of a cuboid.h]h/Rotation of a cuboid.}(hjKh jKubah}(h]h]h]h]h]uhj-h!h"hMh jKubeh}(h](id172jKeh]h] fig9-2-14ah]h]jEcenteruhjhMh jJhhh!h"j}jKjKsj}jKjKsubhM)}(hXL:numref:`fig9-2-14` illustrates the configuration generated using this
specification. Note that clockwise rotation was performed by specifying
a negative angle. In this case, the centroid of the inner cuboid
coincides with (0,0); however, the same geometric rotation would have
occurred if the bodies had not been centered at (0,0).h](j)}(h:numref:`fig9-2-14`h]jM)}(hjKh]h/ fig9-2-14}(hhh jKubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jKubah}(h]h]h]h]h]refdochj refdomainjKreftypenumrefrefexplicitrefwarnjW fig9-2-14uhjh!h"hMh jKubh/X9 illustrates the configuration generated using this
specification. Note that clockwise rotation was performed by specifying
a negative angle. In this case, the centroid of the inner cuboid
coincides with (0,0); however, the same geometric rotation would have
occurred if the bodies had not been centered at (0,0).}(hX9 illustrates the configuration generated using this
specification. Note that clockwise rotation was performed by specifying
a negative angle. In this case, the centroid of the inner cuboid
coincides with (0,0); however, the same geometric rotation would have
occurred if the bodies had not been centered at (0,0).h jKhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jJhhubh)}(h.. _9-2-3-6-1-11:h]h}(h]h]h]h]h]hid77uhh
hMh jJhhh!h"ubeh}(h](rotatejJeh]h](rotate9-2-3-6-1-10eh]h]uhh#h jAhhh!h"hMcj}jLjJsj}jJjJsubh$)}(hhh](h))}(hChordh]h/Chord}(hjLh jLhhh!NhNubah}(h]h]h]h]h]uhh(h jLhhh!h"hMubhM)}(hXThe *chord* modifier is used to remove a portion of a body. It provides
for horizontal and/or vertical cuts on a body, with the portion of the
body on a specified side of that body discarded. Chords may be applied
to cylinders or hexprisms but may not be applied to cuboids. (Such
“cuts” may be explicitly defined in the body definition.) The format of
the specification combines the selection of the plane (horizontal or
vertical cut), location of the plane, and the portion of the body to be
retained, all in one terse modifier.h](h/The }(hThe h j)Lhhh!NhNubj)}(h*chord*h]h/chord}(hhh j2Lubah}(h]h]h]h]h]uhjh j)Lubh/X modifier is used to remove a portion of a body. It provides
for horizontal and/or vertical cuts on a body, with the portion of the
body on a specified side of that body discarded. Chords may be applied
to cylinders or hexprisms but may not be applied to cuboids. (Such
“cuts” may be explicitly defined in the body definition.) The format of
the specification combines the selection of the plane (horizontal or
vertical cut), location of the plane, and the portion of the body to be
retained, all in one terse modifier.}(hX modifier is used to remove a portion of a body. It provides
for horizontal and/or vertical cuts on a body, with the portion of the
body on a specified side of that body discarded. Chords may be applied
to cylinders or hexprisms but may not be applied to cuboids. (Such
“cuts” may be explicitly defined in the body definition.) The format of
the specification combines the selection of the plane (horizontal or
vertical cut), location of the plane, and the portion of the body to be
retained, all in one terse modifier.h j)Lhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jLhhubhM)}(hAThe four possible chord specifications for a body are as follows:h]h/AThe four possible chord specifications for a body are as follows:}(hjMLh jKLhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jLhhubjH)}(h?chord +x=xplane
chord +y=yplane
chord -x=xplane
chord -y=yplaneh]h/?chord +x=xplane
chord +y=yplane
chord -x=xplane
chord -y=yplane}(hhh jYLubah}(h]h]h]h]h]j=j>uhjGh!h"hMh jLhhubhM)}(hXwhere *xplane* and *yplane* are the ordinates on the x and y axes,
respectively. The sign on x and y indicates the portion of the body to
be retained after the cut. A plus (+) sign indicates that the portion of
the body in the positive (increasing x or y) direction should be kept,
and a minus (–) sign indicates that the portion of the body in the
negative direction of the cut plane (decreasing x or y) direction is
retained. Chords are applied **after** any translation (*origin*) or
rotation (*rotate*) modifier operations. Multiple chords may be
specified for a single body to obtain multiple cuts. The keyword *chord*
**must** precede each specification.h](h/where }(hwhere h jgLhhh!NhNubj)}(h*xplane*h]h/xplane}(hhh jpLubah}(h]h]h]h]h]uhjh jgLubh/ and }(h and h jgLhhh!NhNubj)}(h*yplane*h]h/yplane}(hhh jLubah}(h]h]h]h]h]uhjh jgLubh/X are the ordinates on the x and y axes,
respectively. The sign on x and y indicates the portion of the body to
be retained after the cut. A plus (+) sign indicates that the portion of
the body in the positive (increasing x or y) direction should be kept,
and a minus (–) sign indicates that the portion of the body in the
negative direction of the cut plane (decreasing x or y) direction is
retained. Chords are applied }(hX are the ordinates on the x and y axes,
respectively. The sign on x and y indicates the portion of the body to
be retained after the cut. A plus (+) sign indicates that the portion of
the body in the positive (increasing x or y) direction should be kept,
and a minus (–) sign indicates that the portion of the body in the
negative direction of the cut plane (decreasing x or y) direction is
retained. Chords are applied h jgLhhh!NhNubh)}(h **after**h]h/after}(hhh jLubah}(h]h]h]h]h]uhhh jgLubh/ any translation (}(h any translation (h jgLhhh!NhNubj)}(h*origin*h]h/origin}(hhh jLubah}(h]h]h]h]h]uhjh jgLubh/) or
rotation (}(h) or
rotation (h jgLhhh!NhNubj)}(h*rotate*h]h/rotate}(hhh jLubah}(h]h]h]h]h]uhjh jgLubh/o) modifier operations. Multiple chords may be
specified for a single body to obtain multiple cuts. The keyword }(ho) modifier operations. Multiple chords may be
specified for a single body to obtain multiple cuts. The keyword h jgLhhh!NhNubj)}(h*chord*h]h/chord}(hhh jLubah}(h]h]h]h]h]uhjh jgLubh/
}(h
h jgLhhh!NhNubh)}(h**must**h]h/must}(hhh jLubah}(h]h]h]h]h]uhhh jgLubh/ precede each specification.}(h precede each specification.h jgLhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jLhhubhM)}(hThe use of chords is best illustrated by example. :numref:`fig9-2-15` through
:numref:`fig9-2-18` show unit body descriptions with various chord
specifications.h](h/2The use of chords is best illustrated by example. }(h2The use of chords is best illustrated by example. h jLhhh!NhNubj)}(h:numref:`fig9-2-15`h]jM)}(hjMh]h/ fig9-2-15}(hhh jMubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jMubah}(h]h]h]h]h]refdochj refdomainjMreftypenumrefrefexplicitrefwarnjW fig9-2-15uhjh!h"hMh jLubh/ through
}(h through
h jLhhh!NhNubj)}(h:numref:`fig9-2-18`h]jM)}(hj+Mh]h/ fig9-2-18}(hhh j-Mubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh j)Mubah}(h]h]h]h]h]refdochj refdomainj7MreftypenumrefrefexplicitrefwarnjW fig9-2-18uhjh!h"hMh jLubh/? show unit body descriptions with various chord
specifications.}(h? show unit body descriptions with various chord
specifications.h jLhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jLhhubh)}(h.. _fig9-2-15:h]h}(h]h]h]h]h]h fig9-2-15uhh
hMh jLhhh!h"ubj)}(hhh](j)}(h`.. figure:: figs/NEWT/fig15.png
:align: center
:width: 500
Example of chord +x behavior.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig15.pngj*}j,joMsuhjh j_Mh!h"hMubj.)}(hExample of chord +x behavior.h]h/Example of chord +x behavior.}(hjsMh jqMubah}(h]h]h]h]h]uhj-h!h"hMh j_Mubeh}(h](id173j^Meh]h] fig9-2-15ah]h]jEcenteruhjhMh jLhhh!h"j}jMjTMsj}j^MjTMsubh)}(h.. _fig9-2-16:h]h}(h]h]h]h]h]h fig9-2-16uhh
hMh jLhhh!h"ubj)}(hhh](j)}(h`.. figure:: figs/NEWT/fig16.png
:align: center
:width: 500
Example of chord -y behavior.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig16.pngj*}j,jMsuhjh jMh!h"hMubj.)}(hExample of chord -y behavior.h]h/Example of chord -y behavior.}(hjMh jMubah}(h]h]h]h]h]uhj-h!h"hMh jMubeh}(h](id174jMeh]h] fig9-2-16ah]h]jEcenteruhjhMh jLhhh!h"j}jMjMsj}jMjMsubh)}(h.. _fig9-2-17:h]h}(h]h]h]h]h]h fig9-2-17uhh
hMh jLhhh!h"ubj)}(hhh](j)}(hw.. figure:: figs/NEWT/fig17.png
:align: center
:width: 500
Use of two chords to create a quarter-cylinder body.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig17.pngj*}j,jMsuhjh jMh!h"hMubj.)}(h4Use of two chords to create a quarter-cylinder body.h]h/4Use of two chords to create a quarter-cylinder body.}(hjMh jMubah}(h]h]h]h]h]uhj-h!h"hMh jMubeh}(h](id175jMeh]h] fig9-2-17ah]h]jEcenteruhjhMh jLhhh!h"j}jMjMsj}jMjMsubh)}(h.. _fig9-2-18:h]h}(h]h]h]h]h]h fig9-2-18uhh
hMh jLhhh!h"ubj)}(hhh](j)}(h|.. figure:: figs/NEWT/fig18.png
:align: center
:width: 500
Use of four chords on a cylinder to create a square body.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig18.pngj*}j,jNsuhjh jNh!h"hMubj.)}(h9Use of four chords on a cylinder to create a square body.h]h/9Use of four chords on a cylinder to create a square body.}(hjNh jNubah}(h]h]h]h]h]uhj-h!h"hMh jNubeh}(h](id176jNeh]h] fig9-2-18ah]h]jEcenteruhjhMh jLhhh!h"j}j&NjMsj}jNjMsubhM)}(hXIn :numref:`fig9-2-15`, a chord is placed at x=0 and the positive portion
relative to the chord (x >0) is retained because +x mode is specified.
Since the cylinder is centered at (0, 0), this chord cuts the cylinder
in half and retains the right half of the cylinder. The unit in
:numref:`fig9-2-16` uses the same cylinder but with a chord cutting at the
plane located at y=0. The bottom half (y < 0) is kept because –y is
specified.h](h/In }(hIn h j,Nhhh!NhNubj)}(h:numref:`fig9-2-15`h]jM)}(hj7Nh]h/ fig9-2-15}(hhh j9Nubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh j5Nubah}(h]h]h]h]h]refdochj refdomainjCNreftypenumrefrefexplicitrefwarnjW fig9-2-15uhjh!h"hMh j,Nubh/X, a chord is placed at x=0 and the positive portion
relative to the chord (x >0) is retained because +x mode is specified.
Since the cylinder is centered at (0, 0), this chord cuts the cylinder
in half and retains the right half of the cylinder. The unit in
}(hX, a chord is placed at x=0 and the positive portion
relative to the chord (x >0) is retained because +x mode is specified.
Since the cylinder is centered at (0, 0), this chord cuts the cylinder
in half and retains the right half of the cylinder. The unit in
h j,Nhhh!NhNubj)}(h:numref:`fig9-2-16`h]jM)}(hj\Nh]h/ fig9-2-16}(hhh j^Nubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jZNubah}(h]h]h]h]h]refdochj refdomainjhNreftypenumrefrefexplicitrefwarnjW fig9-2-16uhjh!h"hMh j,Nubh/ uses the same cylinder but with a chord cutting at the
plane located at y=0. The bottom half (y < 0) is kept because –y is
specified.}(h uses the same cylinder but with a chord cutting at the
plane located at y=0. The bottom half (y < 0) is kept because –y is
specified.h j,Nhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jLhhubhM)}(hX:numref:`fig9-2-17` is somewhat more complicated but represents perhaps the
most common use of chords in lattice models. In this case, it is
desired to create a one-quarter cylinder located in the bottom right
quadrant of a cuboid. A 1 by 1 cm square cuboid is centered at (0, 0),
and a cylinder is placed at
(0.5, –0.5), which is the lower right-hand corner of the cuboid. Since
we are interested only in the portion of the cylinder within the
cuboid, we choose to keep the top (+x) and left (–y) portions of the
cylinder. This requires two separate chord modifiers. (Each chord
specifies only one cutting plane.) Additionally, because the cylinder
was relocated to a new origin, the chords are specified such that the
cuts go through the new origin.h](j)}(h:numref:`fig9-2-17`h]jM)}(hjNh]h/ fig9-2-17}(hhh jNubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jNubah}(h]h]h]h]h]refdochj refdomainjNreftypenumrefrefexplicitrefwarnjW fig9-2-17uhjh!h"hMh jNubh/X is somewhat more complicated but represents perhaps the
most common use of chords in lattice models. In this case, it is
desired to create a one-quarter cylinder located in the bottom right
quadrant of a cuboid. A 1 by 1 cm square cuboid is centered at (0, 0),
and a cylinder is placed at
(0.5, –0.5), which is the lower right-hand corner of the cuboid. Since
we are interested only in the portion of the cylinder within the
cuboid, we choose to keep the top (+x) and left (–y) portions of the
cylinder. This requires two separate chord modifiers. (Each chord
specifies only one cutting plane.) Additionally, because the cylinder
was relocated to a new origin, the chords are specified such that the
cuts go through the new origin.}(hX is somewhat more complicated but represents perhaps the
most common use of chords in lattice models. In this case, it is
desired to create a one-quarter cylinder located in the bottom right
quadrant of a cuboid. A 1 by 1 cm square cuboid is centered at (0, 0),
and a cylinder is placed at
(0.5, –0.5), which is the lower right-hand corner of the cuboid. Since
we are interested only in the portion of the cylinder within the
cuboid, we choose to keep the top (+x) and left (–y) portions of the
cylinder. This requires two separate chord modifiers. (Each chord
specifies only one cutting plane.) Additionally, because the cylinder
was relocated to a new origin, the chords are specified such that the
cuts go through the new origin.h jNhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jLhhubhM)}(hXNote that there is no requirement that a chord cut through the origin of
a body. :numref:`fig9-2-18` illustrates the use of four chords to set four
cutting planes. A 0.5 cm cylinder is specified centered within the unit
cuboid. All four of the four permitted cutting planes are specified. We
have effectively created a cuboid by retaining the portion of the
cylinder above (+y) the xz plane located at y= –0.25, below (–y) the
plane at y=+0.25, to the right (+x) of the yz plane at x= –0.25, and to
the left (–x) of the plane located at x=+0.25. There is, of course, a
much more direct means to create a cuboid—this example is provided only
for illustrative purposes.h](h/QNote that there is no requirement that a chord cut through the origin of
a body. }(hQNote that there is no requirement that a chord cut through the origin of
a body. h jNhhh!NhNubj)}(h:numref:`fig9-2-18`h]jM)}(hjNh]h/ fig9-2-18}(hhh jNubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jNubah}(h]h]h]h]h]refdochj refdomainjNreftypenumrefrefexplicitrefwarnjW fig9-2-18uhjh!h"hMh jNubh/XD illustrates the use of four chords to set four
cutting planes. A 0.5 cm cylinder is specified centered within the unit
cuboid. All four of the four permitted cutting planes are specified. We
have effectively created a cuboid by retaining the portion of the
cylinder above (+y) the xz plane located at y= –0.25, below (–y) the
plane at y=+0.25, to the right (+x) of the yz plane at x= –0.25, and to
the left (–x) of the plane located at x=+0.25. There is, of course, a
much more direct means to create a cuboid—this example is provided only
for illustrative purposes.}(hXD illustrates the use of four chords to set four
cutting planes. A 0.5 cm cylinder is specified centered within the unit
cuboid. All four of the four permitted cutting planes are specified. We
have effectively created a cuboid by retaining the portion of the
cylinder above (+y) the xz plane located at y= –0.25, below (–y) the
plane at y=+0.25, to the right (+x) of the yz plane at x= –0.25, and to
the left (–x) of the plane located at x=+0.25. There is, of course, a
much more direct means to create a cuboid—this example is provided only
for illustrative purposes.h jNhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jLhhubhM)}(hXFor guidance on how to cut a cylinder at an oblique angle, refer to
:ref:`9-2-3-6-1-14`.h](h/DFor guidance on how to cut a cylinder at an oblique angle, refer to
}(hDFor guidance on how to cut a cylinder at an oblique angle, refer to
h jNhhh!NhNubj)}(h:ref:`9-2-3-6-1-14`h]j)}(hjNh]h/9-2-3-6-1-14}(hhh jNubah}(h]h](jEstdstd-refeh]h]h]uhjh jNubah}(h]h]h]h]h]refdochj refdomainjNreftyperefrefexplicitrefwarnjW9-2-3-6-1-14uhjh!h"hMh jNubh/.}(hhh jNhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jLhhubh)}(h.. _9-2-3-6-1-12:h]h}(h]h]h]h]h]hid78uhh
hMh jLhhh!h"ubeh}(h](chordjLeh]h](chord9-2-3-6-1-11eh]h]uhh#h jAhhh!h"hMj}j,OjLsj}jLjLsubh$)}(hhh](h))}(hComh]h/Com}(hj6Oh j4Ohhh!NhNubah}(h]h]h]h]h]uhh(h j1Ohhh!h"hMubhM)}(hX%The *com* modifier is a means to label specific bodies. It is provided
primarily for consistency with KENO‑VI. At this time, NEWT simply reads
and then ignores *com* data. It can, however, be used as a means to help
annotate an input listing. The format for the *com* modifier is as
follows:h](h/The }(hThe h jBOhhh!NhNubj)}(h*com*h]h/com}(hhh jKOubah}(h]h]h]h]h]uhjh jBOubh/ modifier is a means to label specific bodies. It is provided
primarily for consistency with KENO‑VI. At this time, NEWT simply reads
and then ignores }(h modifier is a means to label specific bodies. It is provided
primarily for consistency with KENO‑VI. At this time, NEWT simply reads
and then ignores h jBOhhh!NhNubj)}(h*com*h]h/com}(hhh j^Oubah}(h]h]h]h]h]uhjh jBOubh/a data. It can, however, be used as a means to help
annotate an input listing. The format for the }(ha data. It can, however, be used as a means to help
annotate an input listing. The format for the h jBOhhh!NhNubj)}(h*com*h]h/com}(hhh jqOubah}(h]h]h]h]h]uhjh jBOubh/ modifier is as
follows:}(h modifier is as
follows:h jBOhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j1OhhubjH)}(hcom=”comment string”h]h/com=”comment string”}(hhh jOubah}(h]h]h]h]h]j=j>uhjGh!h"hMh j1OhhubhM)}(hwhere *“comment string”* is any text description of up to 132
characters, delimited by single (′) or double quotes (″). For example,
the input description of :numref:`fig9-2-18` is shown here with comments added
via *com* modifiers.h](h/where }(hwhere h jOhhh!NhNubj)}(h*“comment string”*h]h/“comment string”}(hhh jOubah}(h]h]h]h]h]uhjh jOubh/ is any text description of up to 132
characters, delimited by single (′) or double quotes (″). For example,
the input description of }(h is any text description of up to 132
characters, delimited by single (′) or double quotes (″). For example,
the input description of h jOhhh!NhNubj)}(h:numref:`fig9-2-18`h]jM)}(hjOh]h/ fig9-2-18}(hhh jOubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jOubah}(h]h]h]h]h]refdochj refdomainjOreftypenumrefrefexplicitrefwarnjW fig9-2-18uhjh!h"hM h jOubh/' is shown here with comments added
via }(h' is shown here with comments added
via h jOhhh!NhNubj)}(h*com*h]h/com}(hhh jOubah}(h]h]h]h]h]uhjh jOubh/ modifiers.}(h modifiers.h jOhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM h j1OhhubjH)}(hunit 10
cuboid 1 0.5 -0.5 0.5 -0.5 com=”unit cuboid centered at (0,0)”
cylinder 2 0.5 com=”cylinder with four chords”
chord -x=0.25 chord +x=-0.25
chord -y=0.25 chord +y=-0.25h]h/unit 10
cuboid 1 0.5 -0.5 0.5 -0.5 com=”unit cuboid centered at (0,0)”
cylinder 2 0.5 com=”cylinder with four chords”
chord -x=0.25 chord +x=-0.25
chord -y=0.25 chord +y=-0.25}(hhh jOubah}(h]h]h]h]h]j=j>uhjGh!h"hM h j1Ohhubh)}(h.. _9-2-3-6-1-13:h]h}(h]h]h]h]h]hid79uhh
hM h j1Ohhh!h"ubeh}(h](comj%Oeh]h](com9-2-3-6-1-12eh]h]uhh#h jAhhh!h"hMj}jPjOsj}j%OjOsubh$)}(hhh](h))}(hSidesh]h/Sides}(hjPh jPhhh!NhNubah}(h]h]h]h]h]uhh(h jPhhh!h"hM ubhM)}(hXThe *sides* modifier applies only to cylinders and is unique to NEWT
(i.e., it is not used in KENO-VI). Because NEWT’s solution grid is based
on arbitrary polygons, all cells must be straight sided. Hence, the
curved surfaces of a cylinder are approximated as an N-sided regular
polygon. By default, N=12. The *sides* operator allows the user to
override the default. The format is very simple:h](h/The }(hThe h j'Phhh!NhNubj)}(h*sides*h]h/sides}(hhh j0Pubah}(h]h]h]h]h]uhjh j'Pubh/X0 modifier applies only to cylinders and is unique to NEWT
(i.e., it is not used in KENO-VI). Because NEWT’s solution grid is based
on arbitrary polygons, all cells must be straight sided. Hence, the
curved surfaces of a cylinder are approximated as an N-sided regular
polygon. By default, N=12. The }(hX0 modifier applies only to cylinders and is unique to NEWT
(i.e., it is not used in KENO-VI). Because NEWT’s solution grid is based
on arbitrary polygons, all cells must be straight sided. Hence, the
curved surfaces of a cylinder are approximated as an N-sided regular
polygon. By default, N=12. The h j'Phhh!NhNubj)}(h*sides*h]h/sides}(hhh jCPubah}(h]h]h]h]h]uhjh j'Pubh/M operator allows the user to
override the default. The format is very simple:}(hM operator allows the user to
override the default. The format is very simple:h j'Phhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM h jPhhubjH)}(hsides=Nh]h/sides=N}(hhh j\Pubah}(h]h]h]h]h]j=j>uhjGh!h"hM h jPhhubhM)}(hX<where N is the number of sides desired for the full cylinder. In
general, a 12-sided polygon provides an adequate approximation of a
cylinder. Use of additional sides will create a cylinder that has a
smoother appearance and increase the computational effort required to
solve the cells associated with the cylinder.h]h/X<where N is the number of sides desired for the full cylinder. In
general, a 12-sided polygon provides an adequate approximation of a
cylinder. Use of additional sides will create a cylinder that has a
smoother appearance and increase the computational effort required to
solve the cells associated with the cylinder.}(hjlPh jjPhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM h jPhhubhM)}(hX:numref:`fig9-2-19` shows a model built with three nested cylinders inside a
unit cuboid. Cylinder 10 is the innermost cylinder, with no *sides*
modifier; hence, it uses the default 12-sided approximation. The second
cylinder is specified with sides=16; the refinement in this
approximation is seen in the figure. Finally, cylinder 30 is specified
with 40 sides—this is visually a very close approximation to a cylinder.h](j)}(h:numref:`fig9-2-19`h]jM)}(hj~Ph]h/ fig9-2-19}(hhh jPubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh j|Pubah}(h]h]h]h]h]refdochj refdomainjPreftypenumrefrefexplicitrefwarnjW fig9-2-19uhjh!h"hM$ h jxPubh/w shows a model built with three nested cylinders inside a
unit cuboid. Cylinder 10 is the innermost cylinder, with no }(hw shows a model built with three nested cylinders inside a
unit cuboid. Cylinder 10 is the innermost cylinder, with no h jxPhhh!NhNubj)}(h*sides*h]h/sides}(hhh jPubah}(h]h]h]h]h]uhjh jxPubh/X
modifier; hence, it uses the default 12-sided approximation. The second
cylinder is specified with sides=16; the refinement in this
approximation is seen in the figure. Finally, cylinder 30 is specified
with 40 sides—this is visually a very close approximation to a cylinder.}(hX
modifier; hence, it uses the default 12-sided approximation. The second
cylinder is specified with sides=16; the refinement in this
approximation is seen in the figure. Finally, cylinder 30 is specified
with 40 sides—this is visually a very close approximation to a cylinder.h jxPhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM$ h jPhhubh)}(h.. _fig9-2-19:h]h}(h]h]h]h]h]h fig9-2-19uhh
hM+ h jPhhh!h"ubj)}(hhh](j)}(hk.. figure:: figs/NEWT/fig19.png
:align: center
:width: 500
Use of the sides modifier for cylinders.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig19.pngj*}j,jPsuhjh jPh!h"hM0 ubj.)}(h(Use of the sides modifier for cylinders.h]h/(Use of the sides modifier for cylinders.}(hjPh jPubah}(h]h]h]h]h]uhj-h!h"hM0 h jPubeh}(h](id177jPeh]h] fig9-2-19ah]h]jEcenteruhjhM0 h jPhhh!h"j}jPjPsj}jPjPsubh)}(h.. _9-2-3-6-1-14:h]h}(h]h]h]h]h]hid80uhh
hM2 h jPhhh!h"ubeh}(h](sidesj
Peh]h](sides9-2-3-6-1-13eh]h]uhh#h jAhhh!h"hM j}jQjPsj}j
PjPsubh$)}(hhh](h))}(hHolesh]h/Holes}(hjQh j Qhhh!NhNubah}(h]h]h]h]h]uhh(h jQhhh!h"hM5 ubhM)}(hX}The next level of complexity within a *unit* is provided through the use
of a *hole* specification. The *hole* specification is simply a means by
which one unit may be placed within another unit. In some instances, a
well-defined set of structures, assembled as a *unit*, needs to be
placed within a larger unit. NEWT provides two methods to do this—holes
and arrays. Arrays are used to place a unit (or a number of similar
units) in a regular repeating pattern within an enclosing unit. A
*hole*, on the other hand, is a means to place a single unit. This is
often used when units being placed do not have a regular repeating
pattern.h](h/&The next level of complexity within a }(h&The next level of complexity within a h jQhhh!NhNubj)}(h*unit*h]h/unit}(hhh j Qubah}(h]h]h]h]h]uhjh jQubh/" is provided through the use
of a }(h" is provided through the use
of a h jQhhh!NhNubj)}(h*hole*h]h/hole}(hhh j3Qubah}(h]h]h]h]h]uhjh jQubh/ specification. The }(h specification. The h jQhhh!NhNubj)}(h*hole*h]h/hole}(hhh jFQubah}(h]h]h]h]h]uhjh jQubh/ specification is simply a means by
which one unit may be placed within another unit. In some instances, a
well-defined set of structures, assembled as a }(h specification is simply a means by
which one unit may be placed within another unit. In some instances, a
well-defined set of structures, assembled as a h jQhhh!NhNubj)}(h*unit*h]h/unit}(hhh jYQubah}(h]h]h]h]h]uhjh jQubh/, needs to be
placed within a larger unit. NEWT provides two methods to do this—holes
and arrays. Arrays are used to place a unit (or a number of similar
units) in a regular repeating pattern within an enclosing unit. A
}(h, needs to be
placed within a larger unit. NEWT provides two methods to do this—holes
and arrays. Arrays are used to place a unit (or a number of similar
units) in a regular repeating pattern within an enclosing unit. A
h jQhhh!NhNubj)}(h*hole*h]h/hole}(hhh jlQubah}(h]h]h]h]h]uhjh jQubh/, on the other hand, is a means to place a single unit. This is
often used when units being placed do not have a regular repeating
pattern.}(h, on the other hand, is a means to place a single unit. This is
often used when units being placed do not have a regular repeating
pattern.h jQhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM7 h jQhhubhM)}(hBThe format for a *hole* specification within a unit is as follows:h](h/The format for a }(hThe format for a h jQhhh!NhNubj)}(h*hole*h]h/hole}(hhh jQubah}(h]h]h]h]h]uhjh jQubh/+ specification within a unit is as follows:}(h+ specification within a unit is as follows:h jQhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMB h jQhhubjH)}(hhole unit_id [modifier_list]h]h/hole unit_id [modifier_list]}(hhh jQubah}(h]h]h]h]h]j=j>uhjGh!h"hMF h jQhhubhM)}(hX6where *unit_id* is the identification number for the unit that is being
placed within the current unit. (A unit cannot be placed within itself.)
Unlike the shapes described earlier, holes do not have a distinct
identification number of their own—they are simply a mechanism to place
a unit defined elsewhere.h](h/where }(hwhere h jQhhh!NhNubj)}(h *unit_id*h]h/unit_id}(hhh jQubah}(h]h]h]h]h]uhjh jQubh/X' is the identification number for the unit that is being
placed within the current unit. (A unit cannot be placed within itself.)
Unlike the shapes described earlier, holes do not have a distinct
identification number of their own—they are simply a mechanism to place
a unit defined elsewhere.}(hX' is the identification number for the unit that is being
placed within the current unit. (A unit cannot be placed within itself.)
Unlike the shapes described earlier, holes do not have a distinct
identification number of their own—they are simply a mechanism to place
a unit defined elsewhere.h jQhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMH h jQhhubhM)}(hXBy default, the *hole* operator places the origin of the new unit at the
origin (0,0) of the current unit. The *origin* modifier may also be used
with a *hole* specification to position the placed unit at a location
other than (0,0) of the current unit. However, placement of the body is
**always** relative to the origin of the original unit, which can be
defined in a number of different ways.h](h/By default, the }(hBy default, the h jQhhh!NhNubj)}(h*hole*h]h/hole}(hhh jQubah}(h]h]h]h]h]uhjh jQubh/Y operator places the origin of the new unit at the
origin (0,0) of the current unit. The }(hY operator places the origin of the new unit at the
origin (0,0) of the current unit. The h jQhhh!NhNubj)}(h*origin*h]h/origin}(hhh jQubah}(h]h]h]h]h]uhjh jQubh/" modifier may also be used
with a }(h" modifier may also be used
with a h jQhhh!NhNubj)}(h*hole*h]h/hole}(hhh jRubah}(h]h]h]h]h]uhjh jQubh/ specification to position the placed unit at a location
other than (0,0) of the current unit. However, placement of the body is
}(h specification to position the placed unit at a location
other than (0,0) of the current unit. However, placement of the body is
h jQhhh!NhNubh)}(h
**always**h]h/always}(hhh jRubah}(h]h]h]h]h]uhhh jQubh/a relative to the origin of the original unit, which can be
defined in a number of different ways.}(ha relative to the origin of the original unit, which can be
defined in a number of different ways.h jQhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMN h jQhhubhM)}(hXHoles are also associated with a particular shape. Hole specifications
must immediately follow the shape into which they are being placed.
Holes redefine the boundaries of a shape by figuratively cutting holes
in that shape into which units are placed. When mixtures are defined for
a given shape (through media specifications, described below), the
mixture is placed throughout the region, except in the space excluded by
the hole placements.h]h/XHoles are also associated with a particular shape. Hole specifications
must immediately follow the shape into which they are being placed.
Holes redefine the boundaries of a shape by figuratively cutting holes
in that shape into which units are placed. When mixtures are defined for
a given shape (through media specifications, described below), the
mixture is placed throughout the region, except in the space excluded by
the hole placements.}(hj4Rh j2Rhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMU h jQhhubhM)}(hXThe *rotate* modifier can also be applied to a hole, as can the *com*
modifier. However, *chord* specifications cannot be used to remove a
portion of a hole. To construct a cylinder that is cut at an oblique
angle, users should construct a cylinder that is cut by a chord and then
use the *hole* operator combined with the *origin* and *rotate*
modifiers to place and rotate the unit to the desired position and
orientation. This can be particularly useful in hexagonal or triangular
geometries.h](h/The }(hThe h j@Rhhh!NhNubj)}(h*rotate*h]h/rotate}(hhh jIRubah}(h]h]h]h]h]uhjh j@Rubh/4 modifier can also be applied to a hole, as can the }(h4 modifier can also be applied to a hole, as can the h j@Rhhh!NhNubj)}(h*com*h]h/com}(hhh j\Rubah}(h]h]h]h]h]uhjh j@Rubh/
modifier. However, }(h
modifier. However, h j@Rhhh!NhNubj)}(h*chord*h]h/chord}(hhh joRubah}(h]h]h]h]h]uhjh j@Rubh/ specifications cannot be used to remove a
portion of a hole. To construct a cylinder that is cut at an oblique
angle, users should construct a cylinder that is cut by a chord and then
use the }(h specifications cannot be used to remove a
portion of a hole. To construct a cylinder that is cut at an oblique
angle, users should construct a cylinder that is cut by a chord and then
use the h j@Rhhh!NhNubj)}(h*hole*h]h/hole}(hhh jRubah}(h]h]h]h]h]uhjh j@Rubh/ operator combined with the }(h operator combined with the h j@Rhhh!NhNubj)}(h*origin*h]h/origin}(hhh jRubah}(h]h]h]h]h]uhjh j@Rubh/ and }(h and h j@Rhhh!NhNubj)}(h*rotate*h]h/rotate}(hhh jRubah}(h]h]h]h]h]uhjh j@Rubh/
modifiers to place and rotate the unit to the desired position and
orientation. This can be particularly useful in hexagonal or triangular
geometries.}(h
modifiers to place and rotate the unit to the desired position and
orientation. This can be particularly useful in hexagonal or triangular
geometries.h j@Rhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM] h jQhhubhM)}(hXAs an example, consider a unit, unit_id=1, consisting of two concentric
cylinders, and a second unit, consisting of two concentric cuboids.
Descriptions for these two units are given below. Note that these are
incomplete unit specifications; other components of the unit
specification have not yet been introduced. However, for the purposes of
this example, incomplete unit specification will suffice.h]h/XAs an example, consider a unit, unit_id=1, consisting of two concentric
cylinders, and a second unit, consisting of two concentric cuboids.
Descriptions for these two units are given below. Note that these are
incomplete unit specifications; other components of the unit
specification have not yet been introduced. However, for the purposes of
this example, incomplete unit specification will suffice.}(hjRh jRhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMf h jQhhubjH)}(hlunit 1
cylinder 12 0.8
cylinder 13 0.6
unit 2
cuboid 12 0.8 -0.8 0.8 -0.8
cuboid 13 0.6 -0.6 0.6 -0.6h]h/lunit 1
cylinder 12 0.8
cylinder 13 0.6
unit 2
cuboid 12 0.8 -0.8 0.8 -0.8
cuboid 13 0.6 -0.6 0.6 -0.6}(hhh jRubah}(h]h]h]h]h]j=j>uhjGh!h"hMo h jQhhubhM)}(hNow suppose that we wished to place two of the unit 1 cells and one of
the unit 2 cells inside unit 3, with unit 2 rotated by 45°. We can
define a cuboid as unit 3 and place the units 1 and 2 inside the cuboid
using *hole* specifications:h](h/Now suppose that we wished to place two of the unit 1 cells and one of
the unit 2 cells inside unit 3, with unit 2 rotated by 45°. We can
define a cuboid as unit 3 and place the units 1 and 2 inside the cuboid
using }(hNow suppose that we wished to place two of the unit 1 cells and one of
the unit 2 cells inside unit 3, with unit 2 rotated by 45°. We can
define a cuboid as unit 3 and place the units 1 and 2 inside the cuboid
using h jRhhh!NhNubj)}(h*hole*h]h/hole}(hhh jRubah}(h]h]h]h]h]uhjh jRubh/ specifications:}(h specifications:h jRhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMw h jQhhubjH)}(h{unit 3
cuboid 10 4.5 0.0 4.5 0.0
hole 1 origin x=1.3 y=1.3
hole 1 origin x=1.3 y=3.3
hole 2 origin x=3.1 y=2.3 rotate a1=45h]h/{unit 3
cuboid 10 4.5 0.0 4.5 0.0
hole 1 origin x=1.3 y=1.3
hole 1 origin x=1.3 y=3.3
hole 2 origin x=3.1 y=2.3 rotate a1=45}(hhh jRubah}(h]h]h]h]h]j=j>uhjGh!h"hM~ h jQhhubhM)}(hXIn this example, a square cuboid is defined such that its lower-left
corner is situated at (0,0). Three hole operations are used: the first
to place unit 1 at (1.3, 1.3), the second to place another instance of
unit 1 2 cm above the first, at (1.3, 3.3). Lastly, unit 2 is placed
inside unit 3 at (3.1, 2.3) and then rotated 45°. :numref:`fig9-2-20`
illustrates how such a unit would appear.h](h/XOIn this example, a square cuboid is defined such that its lower-left
corner is situated at (0,0). Three hole operations are used: the first
to place unit 1 at (1.3, 1.3), the second to place another instance of
unit 1 2 cm above the first, at (1.3, 3.3). Lastly, unit 2 is placed
inside unit 3 at (3.1, 2.3) and then rotated 45°. }(hXOIn this example, a square cuboid is defined such that its lower-left
corner is situated at (0,0). Three hole operations are used: the first
to place unit 1 at (1.3, 1.3), the second to place another instance of
unit 1 2 cm above the first, at (1.3, 3.3). Lastly, unit 2 is placed
inside unit 3 at (3.1, 2.3) and then rotated 45°. h j
Shhh!NhNubj)}(h:numref:`fig9-2-20`h]jM)}(hjSh]h/ fig9-2-20}(hhh jSubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jSubah}(h]h]h]h]h]refdochj refdomainj$SreftypenumrefrefexplicitrefwarnjW fig9-2-20uhjh!h"hM h j
Subh/*
illustrates how such a unit would appear.}(h*
illustrates how such a unit would appear.h j
Shhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM h jQhhubh)}(h.. _fig9-2-20:h]h}(h]h]h]h]h]h fig9-2-20uhh
hM h jQhhh!h"ubj)}(hhh](j)}(hl.. figure:: figs/NEWT/fig20.png
:align: center
:width: 500
Unit placement within a unit using holes.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig20.pngj*}j,j\Ssuhjh jLSh!h"hM ubj.)}(h)Unit placement within a unit using holes.h]h/)Unit placement within a unit using holes.}(hj`Sh j^Subah}(h]h]h]h]h]uhj-h!h"hM h jLSubeh}(h](id178jKSeh]h] fig9-2-20ah]h]jEcenteruhjhM h jQhhh!h"j}jqSjASsj}jKSjASsubh)}(h.. _9-2-3-6-1-15:h]h}(h]h]h]h]h]hid81uhh
hM h jQhhh!h"ubeh}(h](holesjPeh]h](holes9-2-3-6-1-14eh]h]uhh#h jAhhh!h"hM5 j}jSjPsj}jPjPsubh$)}(hhh](h))}(hArray placementh]h/Array placement}(hjSh jShhh!NhNubah}(h]h]h]h]h]uhh(h jShhh!h"hM ubhM)}(hXkAs indicated in the previous section, arrays are a method for arranging
one or more units within another unit. Arrays specifications are
typically used when units are placed in a repeating pattern. While the
*hole* specification is used to place different units within a given
unit, the array placement specification is used to place an *array*
within a unit\ *.*h](h/As indicated in the previous section, arrays are a method for arranging
one or more units within another unit. Arrays specifications are
typically used when units are placed in a repeating pattern. While the
}(hAs indicated in the previous section, arrays are a method for arranging
one or more units within another unit. Arrays specifications are
typically used when units are placed in a repeating pattern. While the
h jShhh!NhNubj)}(h*hole*h]h/hole}(hhh jSubah}(h]h]h]h]h]uhjh jSubh/{ specification is used to place different units within a given
unit, the array placement specification is used to place an }(h{ specification is used to place different units within a given
unit, the array placement specification is used to place an h jShhh!NhNubj)}(h*array*h]h/array}(hhh jSubah}(h]h]h]h]h]uhjh jSubh/
within a unit }(h
within a unit\ h jShhh!NhNubj)}(h*.*h]h/.}(hhh jSubah}(h]h]h]h]h]uhjh jSubeh}(h]h]h]h]h]uhhLh!h"hM h jShhubhM)}(hAll arrays are specified (declaration of size, type, and fill) in the
array data block, as described in :ref:`9-2-3-9`. The array placement
operator is used to locate an array within a unit. The format for the
array placement operator is as follows:h](h/hAll arrays are specified (declaration of size, type, and fill) in the
array data block, as described in }(hhAll arrays are specified (declaration of size, type, and fill) in the
array data block, as described in h jShhh!NhNubj)}(h:ref:`9-2-3-9`h]j)}(hjSh]h/9-2-3-9}(hhh jSubah}(h]h](jEstdstd-refeh]h]h]uhjh jSubah}(h]h]h]h]h]refdochj refdomainjSreftyperefrefexplicitrefwarnjW9-2-3-9uhjh!h"hM h jSubh/. The array placement
operator is used to locate an array within a unit. The format for the
array placement operator is as follows:}(h. The array placement
operator is used to locate an array within a unit. The format for the
array placement operator is as follows:h jShhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM h jShhubjH)}(h'array arrayid body_id place i j xij yijh]h/'array arrayid body_id place i j xij yij}(hhh jTubah}(h]h]h]h]h]j=j>uhjGh!h"hM h jShhubhM)}(hXwhere *arrayid* is the identification number assigned to the array in
the array data block and *body_id* is the identification number of the
*shape* into which the array is placed. The remainder of the array
placement operator is used to fix the position of the array within the
body, identified by *body_id*. A general discussion of this concept
follows, after which the actual placement of the array is described.h](h/where }(hwhere h j#Thhh!NhNubj)}(h *arrayid*h]h/arrayid}(hhh j,Tubah}(h]h]h]h]h]uhjh j#Tubh/P is the identification number assigned to the array in
the array data block and }(hP is the identification number assigned to the array in
the array data block and h j#Thhh!NhNubj)}(h *body_id*h]h/body_id}(hhh j?Tubah}(h]h]h]h]h]uhjh j#Tubh/% is the identification number of the
}(h% is the identification number of the
h j#Thhh!NhNubj)}(h*shape*h]h/shape}(hhh jRTubah}(h]h]h]h]h]uhjh j#Tubh/ into which the array is placed. The remainder of the array
placement operator is used to fix the position of the array within the
body, identified by }(h into which the array is placed. The remainder of the array
placement operator is used to fix the position of the array within the
body, identified by h j#Thhh!NhNubj)}(h *body_id*h]h/body_id}(hhh jeTubah}(h]h]h]h]h]uhjh j#Tubh/k. A general discussion of this concept
follows, after which the actual placement of the array is described.}(hk. A general discussion of this concept
follows, after which the actual placement of the array is described.h j#Thhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM h jShhubhM)}(hXArrays are defined by two dimensioning parameters—the number of rows and
the number of columns. Each element of an array is filled by a unit;
each unit has its own local coordinate system. In other words, one unit
may have the origin (0,0) in its local coordinate system defined as the
lower-left corner while another unit may have its origin defined at its
geometric center. The array itself has no coordinate system; it is
simply a list of relative positions of units, defined by their
row/column position. The *place* directive of the array placement
operator is used to locate the array within the body into which it is
being placed.h](h/XArrays are defined by two dimensioning parameters—the number of rows and
the number of columns. Each element of an array is filled by a unit;
each unit has its own local coordinate system. In other words, one unit
may have the origin (0,0) in its local coordinate system defined as the
lower-left corner while another unit may have its origin defined at its
geometric center. The array itself has no coordinate system; it is
simply a list of relative positions of units, defined by their
row/column position. The }(hXArrays are defined by two dimensioning parameters—the number of rows and
the number of columns. Each element of an array is filled by a unit;
each unit has its own local coordinate system. In other words, one unit
may have the origin (0,0) in its local coordinate system defined as the
lower-left corner while another unit may have its origin defined at its
geometric center. The array itself has no coordinate system; it is
simply a list of relative positions of units, defined by their
row/column position. The h j~Thhh!NhNubj)}(h*place*h]h/place}(hhh jTubah}(h]h]h]h]h]uhjh j~Tubh/u directive of the array placement
operator is used to locate the array within the body into which it is
being placed.}(hu directive of the array placement
operator is used to locate the array within the body into which it is
being placed.h j~Thhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM h jShhubhM)}(hXIn the *place* directive, *i* represents the column (counting from left
to right) and *j* represents the row (counting from bottom to top) of a
specific element of the array. The coordinate system of that specific
unit is used to set the position of the entire array. The coordinates
*x\ ij* and *y\ ij* represent the location in the current unit where the
array is to be placed. Placement occurs by situating the origin of the
unit in column i, row j at coordinate (x:sub:`ij`,y\ :sub:`ij`).
Placement of arrays within a unit is best understood through examples.
Consider three (partial) unit specifications, as defined and illustrated
in :numref:`fig9-2-21`.h](h/In the }(hIn the h jThhh!NhNubj)}(h*place*h]h/place}(hhh jTubah}(h]h]h]h]h]uhjh jTubh/ directive, }(h directive, h jThhh!NhNubj)}(h*i*h]h/i}(hhh jTubah}(h]h]h]h]h]uhjh jTubh/9 represents the column (counting from left
to right) and }(h9 represents the column (counting from left
to right) and h jThhh!NhNubj)}(h*j*h]h/j}(hhh jTubah}(h]h]h]h]h]uhjh jTubh/ represents the row (counting from bottom to top) of a
specific element of the array. The coordinate system of that specific
unit is used to set the position of the entire array. The coordinates
}(h represents the row (counting from bottom to top) of a
specific element of the array. The coordinate system of that specific
unit is used to set the position of the entire array. The coordinates
h jThhh!NhNubj)}(h*x\ ij*h]h/x ij}(hhh jTubah}(h]h]h]h]h]uhjh jTubh/ and }(h and h jThhh!NhNubj)}(h*y\ ij*h]h/y ij}(hhh jTubah}(h]h]h]h]h]uhjh jTubh/ represent the location in the current unit where the
array is to be placed. Placement occurs by situating the origin of the
unit in column i, row j at coordinate (x:sub:}(h represent the location in the current unit where the
array is to be placed. Placement occurs by situating the origin of the
unit in column i, row j at coordinate (x:sub:h jThhh!NhNubh title_reference)}(h`ij`h]h/ij}(hhh j
Uubah}(h]h]h]h]h]uhjUh jTubh/,y }(h,y\ h jThhh!NhNubj)}(h :sub:`ij`h]h/ij}(hhh jUubah}(h]h]h]h]h]uhjh jTubh/).
Placement of arrays within a unit is best understood through examples.
Consider three (partial) unit specifications, as defined and illustrated
in }(h).
Placement of arrays within a unit is best understood through examples.
Consider three (partial) unit specifications, as defined and illustrated
in h jThhh!NhNubj)}(h:numref:`fig9-2-21`h]jM)}(hj2Uh]h/ fig9-2-21}(hhh j4Uubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh j0Uubah}(h]h]h]h]h]refdochj refdomainj>UreftypenumrefrefexplicitrefwarnjW fig9-2-21uhjh!h"hM h jTubh/.}(hhh jThhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM h jShhubh)}(h.. _fig9-2-21:h]h}(h]h]h]h]h]h fig9-2-21uhh
hM h jShhh!h"ubj)}(hhh](j)}(hm.. figure:: figs/NEWT/fig21.png
:align: center
:width: 600
Example of units to be placed in an array.
h]h}(h]h]h]h]h]width600urifigs/NEWT/fig21.pngj*}j,juUsuhjh jeUh!h"hM ubj.)}(h*Example of units to be placed in an array.h]h/*Example of units to be placed in an array.}(hjyUh jwUubah}(h]h]h]h]h]uhj-h!h"hM h jeUubeh}(h](id179jdUeh]h] fig9-2-21ah]h]jEcenteruhjhM h jShhh!h"j}jUjZUsj}jdUjZUsubhM)}(hXsUnit 1 is a simple 1 by 1 cm cuboid with its origin located at its
bottom-left corner; unit 2 is a similar-sized cuboid but with its origin
located at its geometric center and with a cylinder centered in it; and
unit 3 is identical to unit 1 but with a cylinder centered in it.
Units 2 and 3 are identical in structure but use a different local
coordinate system.h]h/XsUnit 1 is a simple 1 by 1 cm cuboid with its origin located at its
bottom-left corner; unit 2 is a similar-sized cuboid but with its origin
located at its geometric center and with a cylinder centered in it; and
unit 3 is identical to unit 1 but with a cylinder centered in it.
Units 2 and 3 are identical in structure but use a different local
coordinate system.}(hjUh jUhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM h jShhubhM)}(hNow assume an array has been defined in the array data block and
assigned *arrayid*\ =50. The relative positions of the units are shown
in :numref:`fig9-2-22`; unit 3 is located in row 1, column 1.h](h/JNow assume an array has been defined in the array data block and
assigned }(hJNow assume an array has been defined in the array data block and
assigned h jUhhh!NhNubj)}(h *arrayid*h]h/arrayid}(hhh jUubah}(h]h]h]h]h]uhjh jUubh/8 =50. The relative positions of the units are shown
in }(h8\ =50. The relative positions of the units are shown
in h jUhhh!NhNubj)}(h:numref:`fig9-2-22`h]jM)}(hjUh]h/ fig9-2-22}(hhh jUubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jUubah}(h]h]h]h]h]refdochj refdomainjUreftypenumrefrefexplicitrefwarnjW fig9-2-22uhjh!h"hM h jUubh/*; unit 3 is located in row 1, column 1.}(h*; unit 3 is located in row 1, column 1.h jUhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM h jShhubhM)}(hWe desire to place this array within a unit 4, a 2 by 2 cm cuboid with
its lower-left corner located at (0,0). Because there are four different
array positions, this array has four possible placements:h]h/We desire to place this array within a unit 4, a 2 by 2 cm cuboid with
its lower-left corner located at (0,0). Because there are four different
array positions, this array has four possible placements:}(hjUh jUhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM h jShhubh)}(h.. _fig9-2-22:h]h}(h]h]h]h]h]h fig9-2-22uhh
hM h jShhh!h"ubj)}(hhh](j)}(h_.. figure:: figs/NEWT/fig22.png
:align: center
:width: 600
Layout of units in array 50.
h]h}(h]h]h]h]h]width600urifigs/NEWT/fig22.pngj*}j,jVsuhjh jUh!h"hM ubj.)}(hLayout of units in array 50.h]h/Layout of units in array 50.}(hjVh jVubah}(h]h]h]h]h]uhj-h!h"hM h jUubeh}(h](id180jUeh]h] fig9-2-22ah]h]jEcenteruhjhM h jShhh!h"j}j#VjUsj}jUjUsubhM)}(hXFor the first example, the unit located in row 1, column 1 (i.e.,
unit 3) is placed such that its origin (its lower-left corner) is
located at (0,0), which is the origin of unit 4. For the second example,
the unit located in column 2, row 1, is placed such that its local
origin, which is in the center of the unit, is located at x=1.5, y=0.5
in the coordinate system of unit 4.h]h/XFor the first example, the unit located in row 1, column 1 (i.e.,
unit 3) is placed such that its origin (its lower-left corner) is
located at (0,0), which is the origin of unit 4. For the second example,
the unit located in column 2, row 1, is placed such that its local
origin, which is in the center of the unit, is located at x=1.5, y=0.5
in the coordinate system of unit 4.}(hj+Vh j)Vhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM h jShhubh)}(h.. _9-2-3-6-2:h]h}(h]h]h]h]h]hid82uhh
hM h jShhh!h"ubeh}(h](array-placementjSeh]h](array placement9-2-3-6-1-15eh]h]uhh#h jAhhh!h"hM j}jHVjwSsj}jSjwSsubeh}(h](bodiesjAeh]h](bodies 9-2-3-6-1eh]h]uhh#h j>hhh!h"hMWj}jSVjAsj}jAjAsubh$)}(hhh](h))}(hMedia specificationsh]h/Media specifications}(hj]Vh j[Vhhh!NhNubah}(h]h]h]h]h]uhh(h jXVhhh!h"hM ubhM)}(hXOA unit is only partially specified by its constituent bodies. At this
point, no composition has been associated with the various regions of
the problem nor has the outer boundary of the unit been defined. This
section provides information on the use of *media* specifications to
define the contents of each shape that has been defined.h](h/A unit is only partially specified by its constituent bodies. At this
point, no composition has been associated with the various regions of
the problem nor has the outer boundary of the unit been defined. This
section provides information on the use of }(hA unit is only partially specified by its constituent bodies. At this
point, no composition has been associated with the various regions of
the problem nor has the outer boundary of the unit been defined. This
section provides information on the use of h jiVhhh!NhNubj)}(h*media*h]h/media}(hhh jrVubah}(h]h]h]h]h]uhjh jiVubh/K specifications to
define the contents of each shape that has been defined.}(hK specifications to
define the contents of each shape that has been defined.h jiVhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM h jXVhhubhM)}(hEach shape statement defines a basic shape, with optional modifiers,
which represents a spatial region within the unit. Assignment of
compositions to regions is performed via *media* specifications.h](h/Each shape statement defines a basic shape, with optional modifiers,
which represents a spatial region within the unit. Assignment of
compositions to regions is performed via }(hEach shape statement defines a basic shape, with optional modifiers,
which represents a spatial region within the unit. Assignment of
compositions to regions is performed via h jVhhh!NhNubj)}(h*media*h]h/media}(hhh jVubah}(h]h]h]h]h]uhjh jVubh/ specifications.}(h specifications.h jVhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM h jXVhhubhM)}(hAs discussed earlier in the introduction to shapes, input processing in
the SGGP is combinatorial. This permits intersection of shapes, and
different compositions (or media) may be assigned to different portions
of intersecting bodies.h]h/As discussed earlier in the introduction to shapes, input processing in
the SGGP is combinatorial. This permits intersection of shapes, and
different compositions (or media) may be assigned to different portions
of intersecting bodies.}(hjVh jVhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM h jXVhhubhM)}(h2The format of a media specification is as follows:h]h/2The format of a media specification is as follows:}(hjVh jVhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM h jXVhhubjH)}(h3media materialid bias_placeholder reg_def_vectorh]h/3media materialid bias_placeholder reg_def_vector}(hhh jVubah}(h]h]h]h]h]j=j>uhjGh!h"hM
h jXVhhubhM)}(hXwhere *materialid* is the composition number being placed in this entry,
*bias_placeholder* is a simple placeholder that is required but not
used, and *reg_def_vector* is the region definition vector used to
define the shape or shapes to which the mixture is assigned.h](h/where }(hwhere h jVhhh!NhNubj)}(h*materialid*h]h/
materialid}(hhh jVubah}(h]h]h]h]h]uhjh jVubh/7 is the composition number being placed in this entry,
}(h7 is the composition number being placed in this entry,
h jVhhh!NhNubj)}(h*bias_placeholder*h]h/bias_placeholder}(hhh jVubah}(h]h]h]h]h]uhjh jVubh/< is a simple placeholder that is required but not
used, and }(h< is a simple placeholder that is required but not
used, and h jVhhh!NhNubj)}(h*reg_def_vector*h]h/reg_def_vector}(hhh jWubah}(h]h]h]h]h]uhjh jVubh/e is the region definition vector used to
define the shape or shapes to which the mixture is assigned.}(he is the region definition vector used to
define the shape or shapes to which the mixture is assigned.h jVhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM
h jXVhhubhM)}(hX5The *bias_placeholder* is used to be as consistent as possible with
KENO-VI input. KENO-VI allows the user to assign biases within the media
assignments to improve the Monte Carlo solution performance. Biases have
no meaning in NEWT, so the field has no meaning. In KENO-VI, if no
special biasing is desired, a value of 1 is assigned. If it is desired
to move models between NEWT and KENO-VI format, a placeholder value of 1
is recommended. However, the value itself has no meaning within NEWT; it
is simply read and ignored. (This may change in a future release.)h](h/The }(hThe h jWhhh!NhNubj)}(h*bias_placeholder*h]h/bias_placeholder}(hhh j(Wubah}(h]h]h]h]h]uhjh jWubh/X is used to be as consistent as possible with
KENO-VI input. KENO-VI allows the user to assign biases within the media
assignments to improve the Monte Carlo solution performance. Biases have
no meaning in NEWT, so the field has no meaning. In KENO-VI, if no
special biasing is desired, a value of 1 is assigned. If it is desired
to move models between NEWT and KENO-VI format, a placeholder value of 1
is recommended. However, the value itself has no meaning within NEWT; it
is simply read and ignored. (This may change in a future release.)}(hX is used to be as consistent as possible with
KENO-VI input. KENO-VI allows the user to assign biases within the media
assignments to improve the Monte Carlo solution performance. Biases have
no meaning in NEWT, so the field has no meaning. In KENO-VI, if no
special biasing is desired, a value of 1 is assigned. If it is desired
to move models between NEWT and KENO-VI format, a placeholder value of 1
is recommended. However, the value itself has no meaning within NEWT; it
is simply read and ignored. (This may change in a future release.)h jWhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM
h jXVhhubhM)}(hXThe region definition vector is used to describe the location of the
composition within the current unit. This is done by providing a list of
shapes for which the media is either “inside” or “outside.” The sense of
the media with respect to a shape is specified by listing the shape
number with a negative sign if “outside” and with a positive (or no)
sign when the media is placed “inside” the shape.h]h/XThe region definition vector is used to describe the location of the
composition within the current unit. This is done by providing a list of
shapes for which the media is either “inside” or “outside.” The sense of
the media with respect to a shape is specified by listing the shape
number with a negative sign if “outside” and with a positive (or no)
sign when the media is placed “inside” the shape.}(hjCWh jAWhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM
h jXVhhubhM)}(hConsider a simple cylinder inside a cuboid. Assume composition 1 is to
be placed inside the cylinder and composition 2 outside the cylinder but
inside the cuboid. The shape and media specifications could have the
following format:h]h/Consider a simple cylinder inside a cuboid. Assume composition 1 is to
be placed inside the cylinder and composition 2 outside the cylinder but
inside the cuboid. The shape and media specifications could have the
following format:}(hjQWh jOWhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM
h jXVhhubjH)}(hPunit 1
cylinder 10 0.5
cuboid 20 1.0 -1.0 1.0 -1.0
media 1 1 10
media 2 1 20 -10h]h/Punit 1
cylinder 10 0.5
cuboid 20 1.0 -1.0 1.0 -1.0
media 1 1 10
media 2 1 20 -10}(hhh j]Wubah}(h]h]h]h]h]j=j>uhjGh!h"hM
h jXVhhubhM)}(hXIn the above example, the first media record places mixture 1 inside all
of shape 10 (the cylinder). The second media entry places mixture 2 in
all regions that are outside shape 10 but inside shape 20. Note also
that a bias placeholder value of 1 is used in each media statement.h]h/XIn the above example, the first media record places mixture 1 inside all
of shape 10 (the cylinder). The second media entry places mixture 2 in
all regions that are outside shape 10 but inside shape 20. Note also
that a bias placeholder value of 1 is used in each media statement.}(hjmWh jkWhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM$
h jXVhhubhM)}(hX2It is necessary to specify media for all regions of the unit. If any
regions remain unassigned, NEWT will stop with an error message. If the
second record had been omitted, regions outside the cylinder would be
unspecified and the code would stop. Note also that if the second media
statement had read onlyh]h/X2It is necessary to specify media for all regions of the unit. If any
regions remain unassigned, NEWT will stop with an error message. If the
second record had been omitted, regions outside the cylinder would be
unspecified and the code would stop. Note also that if the second media
statement had read only}(hj{Wh jyWhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM)
h jXVhhubjH)}(hmedia 2 1 20h]h/media 2 1 20}(hhh jWubah}(h]h]h]h]h]j=j>uhjGh!h"hM1
h jXVhhubhM)}(hXthen composition 2 would have been placed inside all of cuboid 20,
including inside the cylinder 10. The fact that the contents of 10 have
already been specified is ignored. The above statement directs the code
to put mixture 2 everywhere inside the boundaries of the cuboid.h]h/Xthen composition 2 would have been placed inside all of cuboid 20,
including inside the cylinder 10. The fact that the contents of 10 have
already been specified is ignored. The above statement directs the code
to put mixture 2 everywhere inside the boundaries of the cuboid.}(hjWh jWhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM3
h jXVhhubhM)}(hXEach region definition vector combines all specifications with a logical
AND. In other words, the second media record in “``media 2 1 20``” places
composition 2 in all regions that are simultaneously outside shape 10
**and** inside shape 20. Separate media specifications are required to
place a composition in two independent shapes. The following represents
a cuboid with two nonintersecting cylinders.h](h/|Each region definition vector combines all specifications with a logical
AND. In other words, the second media record in “}(h|Each region definition vector combines all specifications with a logical
AND. In other words, the second media record in “h jWhhh!NhNubjM)}(h``media 2 1 20``h]h/media 2 1 20}(hhh jWubah}(h]h]h]h]h]uhjLh jWubh/S” places
composition 2 in all regions that are simultaneously outside shape 10
}(hS” places
composition 2 in all regions that are simultaneously outside shape 10
h jWhhh!NhNubh)}(h**and**h]h/and}(hhh jWubah}(h]h]h]h]h]uhhh jWubh/ inside shape 20. Separate media specifications are required to
place a composition in two independent shapes. The following represents
a cuboid with two nonintersecting cylinders.}(h inside shape 20. Separate media specifications are required to
place a composition in two independent shapes. The following represents
a cuboid with two nonintersecting cylinders.h jWhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM8
h jXVhhubjH)}(hunit 1
cylinder 10 0.4 origin x=0.5
cylinder 20 0.4 origin x=1.5
cuboid 30 2.0 0.0 1.0 -1.0
media 1 1 10
media 1 1 20
media 2 1 30 -10 -20h]h/unit 1
cylinder 10 0.4 origin x=0.5
cylinder 20 0.4 origin x=1.5
cuboid 30 2.0 0.0 1.0 -1.0
media 1 1 10
media 1 1 20
media 2 1 30 -10 -20}(hhh jWubah}(h]h]h]h]h]j=j>uhjGh!h"hMA
h jXVhhubhM)}(hXRA media statement is necessary to place composition 1 inside shape 10; a
similar statement is necessary to place composition 1 inside shape 20.
Finally, all space inside cuboid 30 but outside both 10 and 20 is filled
with composition 2. If one attempted to fill both 10 and 20 with
composition 1 in a single media record, for example,h]h/XRA media statement is necessary to place composition 1 inside shape 10; a
similar statement is necessary to place composition 1 inside shape 20.
Finally, all space inside cuboid 30 but outside both 10 and 20 is filled
with composition 2. If one attempted to fill both 10 and 20 with
composition 1 in a single media record, for example,}(hjWh jWhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMI
h jXVhhubjH)}(hmedia 1 1 10 20h]h/media 1 1 10 20}(hhh jWubah}(h]h]h]h]h]j=j>uhjGh!h"hMQ
h jXVhhubhM)}(hthen an error would occur. The code would attempt to place composition 1
in all space that is simultaneously within shape 10 **and** within shape
20—and no such space exists.h](h/~then an error would occur. The code would attempt to place composition 1
in all space that is simultaneously within shape 10 }(h~then an error would occur. The code would attempt to place composition 1
in all space that is simultaneously within shape 10 h jXhhh!NhNubh)}(h**and**h]h/and}(hhh jXubah}(h]h]h]h]h]uhhh jXubh/, within shape
20—and no such space exists.}(h, within shape
20—and no such space exists.h jXhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMS
h jXVhhubhM)}(hA more common example is the configuration of a fuel pin
(composition 1), gas gap (composition 2), clad (composition 3), and
moderator (composition 4) in a lattice. Consider a pin in a hexagonal
lattice:h]h/A more common example is the configuration of a fuel pin
(composition 1), gas gap (composition 2), clad (composition 3), and
moderator (composition 4) in a lattice. Consider a pin in a hexagonal
lattice:}(hj&Xh j$Xhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMW
h jXVhhubjH)}(hunit 1
cylinder 10 0.4
cylinder 20 0.41
cylinder 30 0.5
hexprism 40 0.8
media 1 1 10
media 2 1 20 -10
media 3 1 30 -20
media 4 1 40 -30h]h/unit 1
cylinder 10 0.4
cylinder 20 0.41
cylinder 30 0.5
hexprism 40 0.8
media 1 1 10
media 2 1 20 -10
media 3 1 30 -20
media 4 1 40 -30}(hhh j2Xubah}(h]h]h]h]h]j=j>uhjGh!h"hM^
h jXVhhubhM)}(hXIn this example, for the hexagonal moderator region outside the clad, it
is sufficient to specify that mixture 4 is inside 40 **and** outside 30.
Although it is true that the moderator is also outside shapes 10 and 20,
it is not necessary to specify this. Logically, since 10 and 20 are
inside 30, then everything outside 30 must be outside 10 and outside 20.
The use of a hexprism in this example is irrelevant. If the outer body
had been a cuboid, the result would have been the same.h](h/In this example, for the hexagonal moderator region outside the clad, it
is sufficient to specify that mixture 4 is inside 40 }(hIn this example, for the hexagonal moderator region outside the clad, it
is sufficient to specify that mixture 4 is inside 40 h j@Xhhh!NhNubh)}(h**and**h]h/and}(hhh jIXubah}(h]h]h]h]h]uhhh j@Xubh/Xa outside 30.
Although it is true that the moderator is also outside shapes 10 and 20,
it is not necessary to specify this. Logically, since 10 and 20 are
inside 30, then everything outside 30 must be outside 10 and outside 20.
The use of a hexprism in this example is irrelevant. If the outer body
had been a cuboid, the result would have been the same.}(hXa outside 30.
Although it is true that the moderator is also outside shapes 10 and 20,
it is not necessary to specify this. Logically, since 10 and 20 are
inside 30, then everything outside 30 must be outside 10 and outside 20.
The use of a hexprism in this example is irrelevant. If the outer body
had been a cuboid, the result would have been the same.h j@Xhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh
h jXVhhubhM)}(hAs a final example, consider a unit with intersecting bodies. It becomes
possible to assign a unique composition to each intersection of shapes
(:numref:`fig9-2-23`).h](h/As a final example, consider a unit with intersecting bodies. It becomes
possible to assign a unique composition to each intersection of shapes
(}(hAs a final example, consider a unit with intersecting bodies. It becomes
possible to assign a unique composition to each intersection of shapes
(h jbXhhh!NhNubj)}(h:numref:`fig9-2-23`h]jM)}(hjmXh]h/ fig9-2-23}(hhh joXubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jkXubah}(h]h]h]h]h]refdochj refdomainjyXreftypenumrefrefexplicitrefwarnjW fig9-2-23uhjh!h"hMp
h jbXubh/).}(h).h jbXhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMp
h jXVhhubh)}(h.. _fig9-2-23:h]h}(h]h]h]h]h]h fig9-2-23uhh
hMt
h jXVhhh!h"ubj)}(hhh](j)}(hl.. figure:: figs/NEWT/fig23.png
:align: center
:width: 500
Media assignments in overlapping regions.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig23.pngj*}j,jXsuhjh jXh!h"hMy
ubj.)}(h)Media assignments in overlapping regions.h]h/)Media assignments in overlapping regions.}(hjXh jXubah}(h]h]h]h]h]uhj-h!h"hMy
h jXubeh}(h](id181jXeh]h] fig9-2-23ah]h]jEcenteruhjhMy
h jXVhhh!h"j}jXjXsj}jXjXsubhM)}(hXIn this model, cylinder 10 is on the right, 20 is the lower left, and 30
is the upper left. Media 1, placed inside cylinder 10 but outside 20 and
30, is represented by the partially filled right-hand side of the right
cylinder. The central region of the unit is filled with composition 4
and represents all areas that are simultaneously within shapes 10, 20,
and 30. The outermost region is everything that is inside 40, but
outside 10, 20, and 30.h]h/XIn this model, cylinder 10 is on the right, 20 is the lower left, and 30
is the upper left. Media 1, placed inside cylinder 10 but outside 20 and
30, is represented by the partially filled right-hand side of the right
cylinder. The central region of the unit is filled with composition 4
and represents all areas that are simultaneously within shapes 10, 20,
and 30. The outermost region is everything that is inside 40, but
outside 10, 20, and 30.}(hjXh jXhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM{
h jXVhhubhM)}(hXMedia statements apply only to shapes, and only to those shapes within
the unit. Holes and array specifications are used to define placement of
one or more units in which media have already been specified in the
corresponding unit definitions. Like shape statements, media statements
may occur in any order. However, if one region is erroneously assigned
two different compositions in two different media statements, the code
will allow this and will proceed with the calculation. The last
specification for a shape will always take precedence. Thus, it is
important that newly developed models be visually inspected using
mixture plots (files named “*.newtmatl.ps”) created using *drawit=yes*
in the parameter block.h](h/XMedia statements apply only to shapes, and only to those shapes within
the unit. Holes and array specifications are used to define placement of
one or more units in which media have already been specified in the
corresponding unit definitions. Like shape statements, media statements
may occur in any order. However, if one region is erroneously assigned
two different compositions in two different media statements, the code
will allow this and will proceed with the calculation. The last
specification for a shape will always take precedence. Thus, it is
important that newly developed models be visually inspected using
mixture plots (files named “}(hXMedia statements apply only to shapes, and only to those shapes within
the unit. Holes and array specifications are used to define placement of
one or more units in which media have already been specified in the
corresponding unit definitions. Like shape statements, media statements
may occur in any order. However, if one region is erroneously assigned
two different compositions in two different media statements, the code
will allow this and will proceed with the calculation. The last
specification for a shape will always take precedence. Thus, it is
important that newly developed models be visually inspected using
mixture plots (files named “h jXhhh!NhNubj)}(h,*.newtmatl.ps”) created using *drawit=yes*h]h/*.newtmatl.ps”) created using *drawit=yes}(hhh jXubah}(h]h]h]h]h]uhjh jXubh/
in the parameter block.}(h
in the parameter block.h jXhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM
h jXVhhubh)}(h.. _9-2-3-6-3:h]h}(h]h]h]h]h]hid83uhh
hM
h jXVhhh!h"ubh$)}(hhh](h))}(h
Unit boundaryh]h/
Unit boundary}(hjYh j
Yhhh!NhNubah}(h]h]h]h]h]uhh(h jYhhh!h"hM
ubhM)}(hXRThe final section of a unit description is the *boundary* specification.
This input record serves two purposes: to specify the shape that defines
the outer bounds of the unit, and hence the shape of the unit, and
(optionally) to specify the underlying grid associated with the unit.
The format of the boundary specification is as follows:h](h//The final section of a unit description is the }(h/The final section of a unit description is the h jYhhh!NhNubj)}(h
*boundary*h]h/boundary}(hhh j!Yubah}(h]h]h]h]h]uhjh jYubh/X specification.
This input record serves two purposes: to specify the shape that defines
the outer bounds of the unit, and hence the shape of the unit, and
(optionally) to specify the underlying grid associated with the unit.
The format of the boundary specification is as follows:}(hX specification.
This input record serves two purposes: to specify the shape that defines
the outer bounds of the unit, and hence the shape of the unit, and
(optionally) to specify the underlying grid associated with the unit.
The format of the boundary specification is as follows:h jYhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM
h jYhhubjH)}(h6boundary body_id [x-discretization y-discretization]h]h/6boundary body_id [x-discretization y-discretization]}(hhh j:Yubah}(h]h]h]h]h]j=j>uhjGh!h"hM
h jYhhubhM)}(hXwhere *body_id* is the identification number for the body that is to
serve as the unit boundary. The *x‑discretization* and
*y-discretization* terms are integers (≥2) that specify the number of
rectangular cells to be placed in the unit in the x-direction and
y-direction, respectively. A grid specification is **required** for the
global unit but is optional for other units. If a grid is specified for
a grid other than the global unit, that grid replaces the base grid. (An
exception to this principle is discussed later.)h](h/where }(hwhere h jHYhhh!NhNubj)}(h *body_id*h]h/body_id}(hhh jQYubah}(h]h]h]h]h]uhjh jHYubh/V is the identification number for the body that is to
serve as the unit boundary. The }(hV is the identification number for the body that is to
serve as the unit boundary. The h jHYhhh!NhNubj)}(h*x‑discretization*h]h/x‑discretization}(hhh jdYubah}(h]h]h]h]h]uhjh jHYubh/ and
}(h and
h jHYhhh!NhNubj)}(h*y-discretization*h]h/y-discretization}(hhh jwYubah}(h]h]h]h]h]uhjh jHYubh/ terms are integers (≥2) that specify the number of
rectangular cells to be placed in the unit in the x-direction and
y-direction, respectively. A grid specification is }(h terms are integers (≥2) that specify the number of
rectangular cells to be placed in the unit in the x-direction and
y-direction, respectively. A grid specification is h jHYhhh!NhNubh)}(h**required**h]h/required}(hhh jYubah}(h]h]h]h]h]uhhh jHYubh/ for the
global unit but is optional for other units. If a grid is specified for
a grid other than the global unit, that grid replaces the base grid. (An
exception to this principle is discussed later.)}(h for the
global unit but is optional for other units. If a grid is specified for
a grid other than the global unit, that grid replaces the base grid. (An
exception to this principle is discussed later.)h jHYhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM
h jYhhubhM)}(hXIn general, grid refinement should be such that cell sizes are on the
order of or smaller than a mean free path for a neutron. Grid spacing
can be easily varied in order to converge on the parameter of interest.
Global factors, such as a system eigenvalue, can tolerate a relatively
coarse grid. However, if fluxes are known to vary rapidly in space, then
a more refined grid may be necessary. NEWT does provide the ability to
locally refine a grid structure so that detail can be modeled where
needed, without having to pay the computational penalty of refining the
grid everywhere. NEWT does place one limit on grid refinement: every
shape, hole, or array placed within a unit must be intersected by at
least one gridline. The grid may be locally defined or part of the
global grid, but it must intersect each body at least once. Thus, if
small geometric shapes are modeled, a detailed grid structure is
generally necessary.h]h/XIn general, grid refinement should be such that cell sizes are on the
order of or smaller than a mean free path for a neutron. Grid spacing
can be easily varied in order to converge on the parameter of interest.
Global factors, such as a system eigenvalue, can tolerate a relatively
coarse grid. However, if fluxes are known to vary rapidly in space, then
a more refined grid may be necessary. NEWT does provide the ability to
locally refine a grid structure so that detail can be modeled where
needed, without having to pay the computational penalty of refining the
grid everywhere. NEWT does place one limit on grid refinement: every
shape, hole, or array placed within a unit must be intersected by at
least one gridline. The grid may be locally defined or part of the
global grid, but it must intersect each body at least once. Thus, if
small geometric shapes are modeled, a detailed grid structure is
generally necessary.}(hjYh jYhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM
h jYhhubhM)}(hX5Examples of boundary specifications follow, as parts of partial unit
specifications. Media descriptions are omitted for simplicity.
Accompanying figures illustrate the grid structure(s) associated with
each specification. :numref:`fig9-2-24` shows a single (global) unit with a 2
by 2 base grid. Cuboid 10 serves as the boundary for the unit. This
represents the minimum grid structure that can be specified for a unit.
:numref:`fig9-2-25` shows a more complex configuration in which a unit defined
with a 5 by 5 grid is placed in the center of a larger enclosing unit,
specified to have a 3 by 3 grid. Note that because the first unit has
its own (local) grid, the underlying grid structure is removed in favor
of the local grid structure. The grid is applied to the boundary shape
of the unit, which is cuboid 10.h](h/Examples of boundary specifications follow, as parts of partial unit
specifications. Media descriptions are omitted for simplicity.
Accompanying figures illustrate the grid structure(s) associated with
each specification. }(hExamples of boundary specifications follow, as parts of partial unit
specifications. Media descriptions are omitted for simplicity.
Accompanying figures illustrate the grid structure(s) associated with
each specification. h jYhhh!NhNubj)}(h:numref:`fig9-2-24`h]jM)}(hjYh]h/ fig9-2-24}(hhh jYubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jYubah}(h]h]h]h]h]refdochj refdomainjYreftypenumrefrefexplicitrefwarnjW fig9-2-24uhjh!h"hM
h jYubh/ shows a single (global) unit with a 2
by 2 base grid. Cuboid 10 serves as the boundary for the unit. This
represents the minimum grid structure that can be specified for a unit.
}(h shows a single (global) unit with a 2
by 2 base grid. Cuboid 10 serves as the boundary for the unit. This
represents the minimum grid structure that can be specified for a unit.
h jYhhh!NhNubj)}(h:numref:`fig9-2-25`h]jM)}(hjYh]h/ fig9-2-25}(hhh jYubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jYubah}(h]h]h]h]h]refdochj refdomainjYreftypenumrefrefexplicitrefwarnjW fig9-2-25uhjh!h"hM
h jYubh/X} shows a more complex configuration in which a unit defined
with a 5 by 5 grid is placed in the center of a larger enclosing unit,
specified to have a 3 by 3 grid. Note that because the first unit has
its own (local) grid, the underlying grid structure is removed in favor
of the local grid structure. The grid is applied to the boundary shape
of the unit, which is cuboid 10.}(hX} shows a more complex configuration in which a unit defined
with a 5 by 5 grid is placed in the center of a larger enclosing unit,
specified to have a 3 by 3 grid. Note that because the first unit has
its own (local) grid, the underlying grid structure is removed in favor
of the local grid structure. The grid is applied to the boundary shape
of the unit, which is cuboid 10.h jYhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM
h jYhhubhM)}(hXY:numref:`fig9-2-26` shows a similar structure; however, the cuboid was removed
from unit 1 and the outer hexprism was defined as the unit boundary.
Note that the grid structure applied to the nonrectangular body is the
same as the one that would be assigned for a cuboid with the same minima
and maxima in x and y directions. :numref:`fig9-2-27` illustrates the grid
structure that would be applied to the same model as was used in the
previous figure but with CMFD acceleration enabled. Because CMFD is
normally applied to a coarse mesh defined by the base global grid
(unless xycmfd=0), the global grid is always retained when CMFD
acceleration is used. Finally, :numref:`fig9-2-28` illustrates the use of a
base grid only. In this case, no grid structure is assigned for unit 1;
the bodies are inlaid but are adapted to the base global grid structure.h](j)}(h:numref:`fig9-2-26`h]jM)}(hjZh]h/ fig9-2-26}(hhh jZubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jZubah}(h]h]h]h]h]refdochj refdomainjZreftypenumrefrefexplicitrefwarnjW fig9-2-26uhjh!h"hM
h j
Zubh/X5 shows a similar structure; however, the cuboid was removed
from unit 1 and the outer hexprism was defined as the unit boundary.
Note that the grid structure applied to the nonrectangular body is the
same as the one that would be assigned for a cuboid with the same minima
and maxima in x and y directions. }(hX5 shows a similar structure; however, the cuboid was removed
from unit 1 and the outer hexprism was defined as the unit boundary.
Note that the grid structure applied to the nonrectangular body is the
same as the one that would be assigned for a cuboid with the same minima
and maxima in x and y directions. h j
Zhhh!NhNubj)}(h:numref:`fig9-2-27`h]jM)}(hj5Zh]h/ fig9-2-27}(hhh j7Zubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh j3Zubah}(h]h]h]h]h]refdochj refdomainjAZreftypenumrefrefexplicitrefwarnjW fig9-2-27uhjh!h"hM
h j
Zubh/X@ illustrates the grid
structure that would be applied to the same model as was used in the
previous figure but with CMFD acceleration enabled. Because CMFD is
normally applied to a coarse mesh defined by the base global grid
(unless xycmfd=0), the global grid is always retained when CMFD
acceleration is used. Finally, }(hX@ illustrates the grid
structure that would be applied to the same model as was used in the
previous figure but with CMFD acceleration enabled. Because CMFD is
normally applied to a coarse mesh defined by the base global grid
(unless xycmfd=0), the global grid is always retained when CMFD
acceleration is used. Finally, h j
Zhhh!NhNubj)}(h:numref:`fig9-2-28`h]jM)}(hjZZh]h/ fig9-2-28}(hhh j\Zubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jXZubah}(h]h]h]h]h]refdochj refdomainjfZreftypenumrefrefexplicitrefwarnjW fig9-2-28uhjh!h"hM
h j
Zubh/ illustrates the use of a
base grid only. In this case, no grid structure is assigned for unit 1;
the bodies are inlaid but are adapted to the base global grid structure.}(h illustrates the use of a
base grid only. In this case, no grid structure is assigned for unit 1;
the bodies are inlaid but are adapted to the base global grid structure.h j
Zhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM
h jYhhubh)}(h.. _fig9-2-24:h]h}(h]h]h]h]h]h fig9-2-24uhh
hM
h jYhhh!h"ubj)}(hhh](j)}(ht.. figure:: figs/NEWT/fig24.png
:align: center
:width: 500
Unit with 2 by 2 grid in a simple pin-cell model.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig24.pngj*}j,jZsuhjh jZh!h"hM
ubj.)}(h1Unit with 2 by 2 grid in a simple pin-cell model.h]h/1Unit with 2 by 2 grid in a simple pin-cell model.}(hjZh jZubah}(h]h]h]h]h]uhj-h!h"hM
h jZubeh}(h](id182jZeh]h] fig9-2-24ah]h]jEcenteruhjhM
h jYhhh!h"j}jZjZsj}jZjZsubh)}(h.. _fig9-2-25:h]h}(h]h]h]h]h]h fig9-2-25uhh
hM
h jYhhh!h"ubj)}(hhh](j)}(hz.. figure:: figs/NEWT/fig26.png
:align: center
:width: 500
Unit with 5 by 5 grid inset into unit with 3 by 3 grid.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig26.pngj*}j,jZsuhjh jZh!h"hM
ubj.)}(h7Unit with 5 by 5 grid inset into unit with 3 by 3 grid.h]h/7Unit with 5 by 5 grid inset into unit with 3 by 3 grid.}(hjZh jZubah}(h]h]h]h]h]uhj-h!h"hM
h jZubeh}(h](id183jZeh]h] fig9-2-25ah]h]jEcenteruhjhM
h jYhhh!h"j}jZjZsj}jZjZsubh)}(h.. _fig9-2-26:h]h}(h]h]h]h]h]h fig9-2-26uhh
hM
h jYhhh!h"ubj)}(hhh](j)}(h.. figure:: figs/NEWT/fig26.png
:align: center
:width: 500
Effect of boundary grid specification on noncuboidal unit placed as a hole within a larger unit.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig26.pngj*}j,j
[suhjh jZh!h"hM
ubj.)}(h`Effect of boundary grid specification on noncuboidal unit placed as a hole within a larger unit.h]h/`Effect of boundary grid specification on noncuboidal unit placed as a hole within a larger unit.}(hj[h j[ubah}(h]h]h]h]h]uhj-h!h"hM
h jZubeh}(h](id184jZeh]h] fig9-2-26ah]h]jEcenteruhjhM
h jYhhh!h"j}j[jZsj}jZjZsubh)}(h.. _fig9-2-27:h]h}(h]h]h]h]h]h fig9-2-27uhh
hM
h jYhhh!h"ubj)}(hhh](j)}(h.. figure:: figs/NEWT/fig27.png
:align: center
:width: 500
Effect of coarse-mesh finite-difference acceleration on grid structure.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig27.pngj*}j,j@[suhjh j0[h!h"hM
ubj.)}(hGEffect of coarse-mesh finite-difference acceleration on grid structure.h]h/GEffect of coarse-mesh finite-difference acceleration on grid structure.}(hjD[h jB[ubah}(h]h]h]h]h]uhj-h!h"hM
h j0[ubeh}(h](id185j/[eh]h] fig9-2-27ah]h]jEcenteruhjhM
h jYhhh!h"j}jU[j%[sj}j/[j%[subh)}(h.. _fig9-2-28:h]h}(h]h]h]h]h]h fig9-2-28uhh
hM
h jYhhh!h"ubj)}(hhh](j)}(hy.. figure:: figs/NEWT/fig28.png
:align: center
:width: 500
Use of base grid without localized grid specification.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig28.pngj*}j,jv[suhjh jf[h!h"hM
ubj.)}(h6Use of base grid without localized grid specification.h]h/6Use of base grid without localized grid specification.}(hjz[h jx[ubah}(h]h]h]h]h]uhj-h!h"hM
h jf[ubeh}(h](id186je[eh]h] fig9-2-28ah]h]jEcenteruhjhM
h jYhhh!h"j}j[j[[sj}je[j[[subhM)}(hThe following section provides examples of complete geometry specifications for
various models, including bodies, media, and boundary specifications. Each will
include one or more uses or boundary specifications for units.h]h/The following section provides examples of complete geometry specifications for
various models, including bodies, media, and boundary specifications. Each will
include one or more uses or boundary specifications for units.}(hj[h j[hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM
h jYhhubh)}(h.. _9-2-3-6-4:h]h}(h]h]h]h]h]hid84uhh
hM
h jYhhh!h"ubeh}(h](
unit-boundaryjYeh]h](
unit boundary 9-2-3-6-3eh]h]uhh#h jXVhhh!h"hM
j}j[jXsj}jYjXsubeh}(h](media-specificationsjAVeh]h](media specifications 9-2-3-6-2eh]h]uhh#h j>hhh!h"hM j}j[j7Vsj}jAVj7Vsubh$)}(hhh](h))}(hGeometry block examplesh]h/Geometry block examples}(hj[h j[hhh!NhNubah}(h]h]h]h]h]uhh(h j[hhh!h"hM
ubhM)}(hThe following three subsections present geometry block examples to show
how various models may be assembled. Each listing is described briefly
and is followed by a figure showing the NEWT grid structure generated
for each set of geometry instructions.h]h/The following three subsections present geometry block examples to show
how various models may be assembled. Each listing is described briefly
and is followed by a figure showing the NEWT grid structure generated
for each set of geometry instructions.}(hj[h j[hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM
h j[hhubh)}(h.. _9-2-3-6-4-1:h]h}(h]h]h]h]h]hid85uhh
hMh j[hhh!h"ubh$)}(hhh](h))}(hSimple pin cellh]h/Simple pin cell}(hj[h j[hhh!NhNubah}(h]h]h]h]h]uhh(h j[hhh!h"hMubhM)}(hXThe following geometry block (:numref:`fig9-2-29`) shows the specifications
necessary to define a single pin-cell. The model is reduced to a ¼ cell
to take advantage of symmetry. Mixture 1 is fuel, mixture 2 is fill gas,
mixture 3 is clad, and mixture 4 is moderator. Features of this model
include the use of chords to obtain ¼ cylinders and the specification of
20 sides for each cylinder (five sides for a ¼ cylinder).h](h/The following geometry block (}(hThe following geometry block (h j[hhh!NhNubj)}(h:numref:`fig9-2-29`h]jM)}(hj\h]h/ fig9-2-29}(hhh j\ubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh j\ubah}(h]h]h]h]h]refdochj refdomainj\reftypenumrefrefexplicitrefwarnjW fig9-2-29uhjh!h"hMh j[ubh/X) shows the specifications
necessary to define a single pin-cell. The model is reduced to a ¼ cell
to take advantage of symmetry. Mixture 1 is fuel, mixture 2 is fill gas,
mixture 3 is clad, and mixture 4 is moderator. Features of this model
include the use of chords to obtain ¼ cylinders and the specification of
20 sides for each cylinder (five sides for a ¼ cylinder).}(hX) shows the specifications
necessary to define a single pin-cell. The model is reduced to a ¼ cell
to take advantage of symmetry. Mixture 1 is fuel, mixture 2 is fill gas,
mixture 3 is clad, and mixture 4 is moderator. Features of this model
include the use of chords to obtain ¼ cylinders and the specification of
20 sides for each cylinder (five sides for a ¼ cylinder).h j[hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j[hhubh)}(h.. _fig9-2-29:h]h}(h]h]h]h]h]h fig9-2-29uhh
hMh j[hhh!h"ubj)}(hhh](j)}(h.. figure:: figs/NEWT/fig29.png
:align: center
:width: 500
Geometry model for infinite-lattice pin cell with fuel, gap, clad, and moderator.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig29.pngj*}j,jJ\suhjh j:\h!h"hMubj.)}(hQGeometry model for infinite-lattice pin cell with fuel, gap, clad, and moderator.h]h/QGeometry model for infinite-lattice pin cell with fuel, gap, clad, and moderator.}(hjN\h jL\ubah}(h]h]h]h]h]uhj-h!h"hMh j:\ubeh}(h](id187j9\eh]h] fig9-2-29ah]h]jEcenteruhjhMh j[hhh!h"j}j_\j/\sj}j9\j/\subh)}(h.. _9-2-3-6-4-2:h]h}(h]h]h]h]h]hid86uhh
hMh j[hhh!h"ubeh}(h](simple-pin-cellj[eh]h](simple pin cell9-2-3-6-4-1eh]h]uhh#h j[hhh!h"hMj}jv\j[sj}j[j[subh$)}(hhh](h))}(hHexagonal assemblyh]h/Hexagonal assembly}(hj\h j~\hhh!NhNubah}(h]h]h]h]h]uhh(h j{\hhh!h"hMubhM)}(hXbThe geometry block below (:numref:`fig9-2-30`) is used to describe a hexagonal
fuel assembly within a hexagonal shroud. Each cylinder is placed
individually, followed by a series of media statements that fill each
cylinder. The hexagonal moderator area is surrounded by a hexagonal
shroud of cladding material. Note that NEWT allows only cuboid and
hexprisms as outer boundaries for the global unit. This model could also
have been assembled with a unit definition for a set of cylinders, which
could then be placed in the global unit using holes or by defining a
single pin cell and placing it using an array.h](h/The geometry block below (}(hThe geometry block below (h j\hhh!NhNubj)}(h:numref:`fig9-2-30`h]jM)}(hj\h]h/ fig9-2-30}(hhh j\ubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh j\ubah}(h]h]h]h]h]refdochj refdomainj\reftypenumrefrefexplicitrefwarnjW fig9-2-30uhjh!h"hMh j\ubh/X5) is used to describe a hexagonal
fuel assembly within a hexagonal shroud. Each cylinder is placed
individually, followed by a series of media statements that fill each
cylinder. The hexagonal moderator area is surrounded by a hexagonal
shroud of cladding material. Note that NEWT allows only cuboid and
hexprisms as outer boundaries for the global unit. This model could also
have been assembled with a unit definition for a set of cylinders, which
could then be placed in the global unit using holes or by defining a
single pin cell and placing it using an array.}(hX5) is used to describe a hexagonal
fuel assembly within a hexagonal shroud. Each cylinder is placed
individually, followed by a series of media statements that fill each
cylinder. The hexagonal moderator area is surrounded by a hexagonal
shroud of cladding material. Note that NEWT allows only cuboid and
hexprisms as outer boundaries for the global unit. This model could also
have been assembled with a unit definition for a set of cylinders, which
could then be placed in the global unit using holes or by defining a
single pin cell and placing it using an array.h j\hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j{\hhubh)}(h.. _fig9-2-30:h]h}(h]h]h]h]h]h fig9-2-30uhh
hM%h j{\hhh!h"ubj)}(hhh](j)}(hm.. figure:: figs/NEWT/fig30.png
:align: center
:width: 500
Geometry model of hexagonal fuel assembly.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig30.pngj*}j,j\suhjh j\h!h"hM*ubj.)}(h*Geometry model of hexagonal fuel assembly.h]h/*Geometry model of hexagonal fuel assembly.}(hj\h j\ubah}(h]h]h]h]h]uhj-h!h"hM*h j\ubeh}(h](id188j\eh]h] fig9-2-30ah]h]jEcenteruhjhM*h j{\hhh!h"j}j\j\sj}j\j\subh)}(h.. _9-2-3-6-4-3:h]h}(h]h]h]h]h]hid87uhh
hM,h j{\hhh!h"ubeh}(h](hexagonal-assemblyjo\eh]h](hexagonal assembly9-2-3-6-4-2eh]h]uhh#h j[hhh!h"hMj}j]je\sj}jo\je\subh$)}(hhh](h))}(h'Advanced CANDU reactor ACR-700 assemblyh]h/'Advanced CANDU reactor ACR-700 assembly}(hj]h j]hhh!NhNubah}(h]h]h]h]h]uhh(h j]hhh!h"hM/ubhM)}(hXThis example of a geometry block (:numref:`fig9-2-31`) is included to illustrate the complexity of design that
is possible through the use of simple bodies, units, and holes. The
ACR-700 design cannot be modeled using an array because pins are not
placed in a repeating lattice pattern. Features of this example include
use of holes; use of noncuboidal units placed in holes; and localized
pin-cell grid refinement by (1) decreased mesh size in fuel elements
(three outer rings) and (2) increased radial discretization (central
pin).h](h/"This example of a geometry block (}(h"This example of a geometry block (h j]hhh!NhNubj)}(h:numref:`fig9-2-31`h]jM)}(hj(]h]h/ fig9-2-31}(hhh j*]ubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh j&]ubah}(h]h]h]h]h]refdochj refdomainj4]reftypenumrefrefexplicitrefwarnjW fig9-2-31uhjh!h"hM1h j]ubh/X) is included to illustrate the complexity of design that
is possible through the use of simple bodies, units, and holes. The
ACR-700 design cannot be modeled using an array because pins are not
placed in a repeating lattice pattern. Features of this example include
use of holes; use of noncuboidal units placed in holes; and localized
pin-cell grid refinement by (1) decreased mesh size in fuel elements
(three outer rings) and (2) increased radial discretization (central
pin).}(hX) is included to illustrate the complexity of design that
is possible through the use of simple bodies, units, and holes. The
ACR-700 design cannot be modeled using an array because pins are not
placed in a repeating lattice pattern. Features of this example include
use of holes; use of noncuboidal units placed in holes; and localized
pin-cell grid refinement by (1) decreased mesh size in fuel elements
(three outer rings) and (2) increased radial discretization (central
pin).h j]hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM1h j]hhubh)}(h.. _fig9-2-31:h]h}(h]h]h]h]h]h fig9-2-31uhh
hM:h j]hhh!h"ubj)}(hhh](j)}(hX9.. figure:: figs/NEWT/fig31.png
:align: center
:width: 500
ACR-700 fuel assembly model.
(continued from :numref:`fig9-2-31`)
::
hole 1
hole 2 origin x=-1.56318 y= 0.75279
hole 2 origin x=-0.38607 y= 1.69150
hole 2 origin x= 1.08176 y= 1.35648
hole 2 origin x= 1.73500
hole 2 origin x= 1.08176 y=-1.35648
hole 2 origin x=-0.38607 y=-1.69150
hole 2 origin x=-1.56318 y=-0.75279
hole 3 origin x=-2.99790 y= 0.68425
hole 3 origin x=-2.40413 y= 1.91723
hole 3 origin x=-1.33419 y= 2.77048
hole 3 origin y= 3.07500
hole 3 origin x= 1.33419 y= 2.77048
hole 3 origin x= 2.40413 y= 1.91723
hole 3 origin x= 2.99790 y= 0.68425
hole 3 origin x= 2.99790 y=-0.68425
hole 3 origin x= 2.40413 y=-1.91723
hole 3 origin x= 1.33419 y=-2.77048
hole 3 origin x= 0.00000 y=-3.07500
hole 3 origin x=-1.33419 y=-2.77048
hole 3 origin x=-2.40413 y=-1.91723
hole 3 origin x=-2.99790 y=-0.68425
hole 4 origin x=-4.33602 y= 0.65355
hole 4 origin x=-3.95075 y= 1.90258
hole 4 origin x=-3.21443 y= 2.98256
hole 4 origin x=-2.19250 y= 3.79752
hole 4 origin x=-0.97575 y= 4.27506
hole 4 origin x= 0.32769 y= 4.37274
hole 4 origin x= 1.60202 y= 4.08188
hole 4 origin x= 2.73400 y= 3.42833
hole 4 origin x= 3.62306 y= 2.47016
hole 4 origin x= 4.19019 y= 1.29250
hole 4 origin x= 4.38500
hole 4 origin x= 4.19019 y=-1.29250
hole 4 origin x= 3.62306 y=-2.47016
hole 4 origin x= 2.73400 y=-3.42833
hole 4 origin x= 1.60202 y=-4.08188
hole 4 origin x= 0.32769 y=-4.37274
hole 4 origin x=-0.97575 y=-4.27506
hole 4 origin x=-2.19250 y=-3.79752
hole 4 origin x=-3.21443 y=-2.98256
hole 4 origin x=-3.95075 y=-1.90258
hole 4 origin x=-4.33602 y=-0.65355
cylinder 501 5.8169 sides=20
cylinder 502 7.55 sides=24
cylinder 503 7.8 sides=24
media 13 1 500
media 5 1 501 -500
media 6 1 502 -501
media 7 1 503 -502
media 8 1 100 -503
boundary 100 50 50
end geom
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig31.pngj*}j,jl]suhjh j\]h!h"hNubj.)}(hACR-700 fuel assembly model.h]h/ACR-700 fuel assembly model.}(hjp]h jn]ubah}(h]h]h]h]h]uhj-h!h"hM?h j\]ubh legend)}(hhh](hM)}(h$(continued from :numref:`fig9-2-31`)h](h/(continued from }(h(continued from h j]ubj)}(h:numref:`fig9-2-31`h]jM)}(hj]h]h/ fig9-2-31}(hhh j]ubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh j]ubah}(h]h]h]h]h]refdochj refdomainj]reftypenumrefrefexplicitrefwarnjW fig9-2-31uhjh!h"hMAh j]ubh/)}(h)h j]ubeh}(h]h]h]h]h]uhhLh!h"hMAh j~]ubjH)}(hXhole 1
hole 2 origin x=-1.56318 y= 0.75279
hole 2 origin x=-0.38607 y= 1.69150
hole 2 origin x= 1.08176 y= 1.35648
hole 2 origin x= 1.73500
hole 2 origin x= 1.08176 y=-1.35648
hole 2 origin x=-0.38607 y=-1.69150
hole 2 origin x=-1.56318 y=-0.75279
hole 3 origin x=-2.99790 y= 0.68425
hole 3 origin x=-2.40413 y= 1.91723
hole 3 origin x=-1.33419 y= 2.77048
hole 3 origin y= 3.07500
hole 3 origin x= 1.33419 y= 2.77048
hole 3 origin x= 2.40413 y= 1.91723
hole 3 origin x= 2.99790 y= 0.68425
hole 3 origin x= 2.99790 y=-0.68425
hole 3 origin x= 2.40413 y=-1.91723
hole 3 origin x= 1.33419 y=-2.77048
hole 3 origin x= 0.00000 y=-3.07500
hole 3 origin x=-1.33419 y=-2.77048
hole 3 origin x=-2.40413 y=-1.91723
hole 3 origin x=-2.99790 y=-0.68425
hole 4 origin x=-4.33602 y= 0.65355
hole 4 origin x=-3.95075 y= 1.90258
hole 4 origin x=-3.21443 y= 2.98256
hole 4 origin x=-2.19250 y= 3.79752
hole 4 origin x=-0.97575 y= 4.27506
hole 4 origin x= 0.32769 y= 4.37274
hole 4 origin x= 1.60202 y= 4.08188
hole 4 origin x= 2.73400 y= 3.42833
hole 4 origin x= 3.62306 y= 2.47016
hole 4 origin x= 4.19019 y= 1.29250
hole 4 origin x= 4.38500
hole 4 origin x= 4.19019 y=-1.29250
hole 4 origin x= 3.62306 y=-2.47016
hole 4 origin x= 2.73400 y=-3.42833
hole 4 origin x= 1.60202 y=-4.08188
hole 4 origin x= 0.32769 y=-4.37274
hole 4 origin x=-0.97575 y=-4.27506
hole 4 origin x=-2.19250 y=-3.79752
hole 4 origin x=-3.21443 y=-2.98256
hole 4 origin x=-3.95075 y=-1.90258
hole 4 origin x=-4.33602 y=-0.65355
cylinder 501 5.8169 sides=20
cylinder 502 7.55 sides=24
cylinder 503 7.8 sides=24
media 13 1 500
media 5 1 501 -500
media 6 1 502 -501
media 7 1 503 -502
media 8 1 100 -503
boundary 100 50 50
end geomh]h/Xhole 1
hole 2 origin x=-1.56318 y= 0.75279
hole 2 origin x=-0.38607 y= 1.69150
hole 2 origin x= 1.08176 y= 1.35648
hole 2 origin x= 1.73500
hole 2 origin x= 1.08176 y=-1.35648
hole 2 origin x=-0.38607 y=-1.69150
hole 2 origin x=-1.56318 y=-0.75279
hole 3 origin x=-2.99790 y= 0.68425
hole 3 origin x=-2.40413 y= 1.91723
hole 3 origin x=-1.33419 y= 2.77048
hole 3 origin y= 3.07500
hole 3 origin x= 1.33419 y= 2.77048
hole 3 origin x= 2.40413 y= 1.91723
hole 3 origin x= 2.99790 y= 0.68425
hole 3 origin x= 2.99790 y=-0.68425
hole 3 origin x= 2.40413 y=-1.91723
hole 3 origin x= 1.33419 y=-2.77048
hole 3 origin x= 0.00000 y=-3.07500
hole 3 origin x=-1.33419 y=-2.77048
hole 3 origin x=-2.40413 y=-1.91723
hole 3 origin x=-2.99790 y=-0.68425
hole 4 origin x=-4.33602 y= 0.65355
hole 4 origin x=-3.95075 y= 1.90258
hole 4 origin x=-3.21443 y= 2.98256
hole 4 origin x=-2.19250 y= 3.79752
hole 4 origin x=-0.97575 y= 4.27506
hole 4 origin x= 0.32769 y= 4.37274
hole 4 origin x= 1.60202 y= 4.08188
hole 4 origin x= 2.73400 y= 3.42833
hole 4 origin x= 3.62306 y= 2.47016
hole 4 origin x= 4.19019 y= 1.29250
hole 4 origin x= 4.38500
hole 4 origin x= 4.19019 y=-1.29250
hole 4 origin x= 3.62306 y=-2.47016
hole 4 origin x= 2.73400 y=-3.42833
hole 4 origin x= 1.60202 y=-4.08188
hole 4 origin x= 0.32769 y=-4.37274
hole 4 origin x=-0.97575 y=-4.27506
hole 4 origin x=-2.19250 y=-3.79752
hole 4 origin x=-3.21443 y=-2.98256
hole 4 origin x=-3.95075 y=-1.90258
hole 4 origin x=-4.33602 y=-0.65355
cylinder 501 5.8169 sides=20
cylinder 502 7.55 sides=24
cylinder 503 7.8 sides=24
media 13 1 500
media 5 1 501 -500
media 6 1 502 -501
media 7 1 503 -502
media 8 1 100 -503
boundary 100 50 50
end geom}(hhh j]ubah}(h]h]h]h]h]j=j>uhjGh!h"hMEh j~]ubeh}(h]h]h]h]h]uhj|]h j\]ubeh}(h](id189j[]eh]h] fig9-2-31ah]h]jEcenteruhjh j]hhh!h"hNj}j]jQ]sj}j[]jQ]subh)}(h.. _9-2-3-6-5:h]h}(h]h]h]h]h]hid88uhh
hM|h j]hhh!h"ubeh}(h]('advanced-candu-reactor-acr-700-assemblyj]eh]h]('advanced candu reactor acr-700 assembly9-2-3-6-4-3eh]h]uhh#h j[hhh!h"hM/j}j]j\sj}j]j\subeh}(h](geometry-block-examplesj[eh]h](geometry block examples 9-2-3-6-4eh]h]uhh#h j>hhh!h"hM
j}j]j[sj}j[j[subh$)}(hhh](h))}(h"Summary of geometry specificationsh]h/"Summary of geometry specifications}(hj]h j]hhh!NhNubah}(h]h]h]h]h]uhh(h j]hhh!h"hMubhM)}(hThis section is provided as a quick reference for geometry statements.
Details and examples of the usage of each geometry specification are
provided in previous subsections of this manual. For each definition,
the lists of permitted modifiers are listed.h]h/This section is provided as a quick reference for geometry statements.
Details and examples of the usage of each geometry specification are
provided in previous subsections of this manual. For each definition,
the lists of permitted modifiers are listed.}(hj^h j^hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh j]hhubh)}(h.. _9-2-3-6-5-1:h]h}(h]h]h]h]h]hid89uhh
hMh j]hhh!h"ubh$)}(hhh](h))}(hUnit definition statementsh]h/Unit definition statements}(hj$^h j"^hhh!NhNubah}(h]h]h]h]h]uhh(h j^hhh!h"hMubjH)}(h[global] unit unit_idh]h/[global] unit unit_id}(hhh j0^ubah}(h]h]h]h]h]j=j>uhjGh!h"hMh j^hhubhM)}(hThe *unit* statement is used to initiate the definition of each unit
used. *unit_id* is an integer identification label for the unit and must
be unique. One (and only one) global unit is required in each geometry
model. Modifiers: none.h](h/The }(hThe h j>^hhh!NhNubj)}(h*unit*h]h/unit}(hhh jG^ubah}(h]h]h]h]h]uhjh j>^ubh/A statement is used to initiate the definition of each unit
used. }(hA statement is used to initiate the definition of each unit
used. h j>^hhh!NhNubj)}(h *unit_id*h]h/unit_id}(hhh jZ^ubah}(h]h]h]h]h]uhjh j>^ubh/ is an integer identification label for the unit and must
be unique. One (and only one) global unit is required in each geometry
model. Modifiers: none.}(h is an integer identification label for the unit and must
be unique. One (and only one) global unit is required in each geometry
model. Modifiers: none.h j>^hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j^hhubjH)}(h4cuboid body_id xmax xmin ymax ymin [modifier_list]h]h/4cuboid body_id xmax xmin ymax ymin [modifier_list]}(hhh js^ubah}(h]h]h]h]h]j=j>uhjGh!h"hMh j^hhubhM)}(hXyThe *cuboid* statement is used to define a rectangular shape. *body_id*
is the integer identification label for the cuboid and must be unique
within the unit it is used. The rectangle is defined such that the
coordinates (x\ :sub:`min`, y\ :sub:`min`) and (x\ :sub:`max`,
y\ :sub:`max`) represent the lower-left and upper-right vertices of the
cuboid. Modifiers: *rotate, com*.h](h/The }(hThe h j^hhh!NhNubj)}(h*cuboid*h]h/cuboid}(hhh j^ubah}(h]h]h]h]h]uhjh j^ubh/2 statement is used to define a rectangular shape. }(h2 statement is used to define a rectangular shape. h j^hhh!NhNubj)}(h *body_id*h]h/body_id}(hhh j^ubah}(h]h]h]h]h]uhjh j^ubh/
is the integer identification label for the cuboid and must be unique
within the unit it is used. The rectangle is defined such that the
coordinates (x }(h
is the integer identification label for the cuboid and must be unique
within the unit it is used. The rectangle is defined such that the
coordinates (x\ h j^hhh!NhNubj)}(h
:sub:`min`h]h/min}(hhh j^ubah}(h]h]h]h]h]uhjh j^ubh/, y }(h, y\ h j^hhh!NhNubj)}(h
:sub:`min`h]h/min}(hhh j^ubah}(h]h]h]h]h]uhjh j^ubh/
) and (x }(h
) and (x\ h j^hhh!NhNubj)}(h
:sub:`max`h]h/max}(hhh j^ubah}(h]h]h]h]h]uhjh j^ubh/,
y }(h,
y\ h j^hhh!NhNubj)}(h
:sub:`max`h]h/max}(hhh j^ubah}(h]h]h]h]h]uhjh j^ubh/N) represent the lower-left and upper-right vertices of the
cuboid. Modifiers: }(hN) represent the lower-left and upper-right vertices of the
cuboid. Modifiers: h j^hhh!NhNubj)}(h
*rotate, com*h]h/rotate, com}(hhh j^ubah}(h]h]h]h]h]uhjh j^ubh/.}(hhh j^hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j^hhubjH)}(h(cylinder body_id radius [modifier_list]h]h/(cylinder body_id radius [modifier_list]}(hhh j_ubah}(h]h]h]h]h]j=j>uhjGh!h"hMh j^hhubhM)}(hThe *cylinder* statement defines a circle with integer label *body_id*
and radius *radius*, placed with its center at the origin (0,0) of the
unit. Modifiers: *origin, rotate, chord, sides, com*.h](h/The }(hThe h j"_hhh!NhNubj)}(h
*cylinder*h]h/cylinder}(hhh j+_ubah}(h]h]h]h]h]uhjh j"_ubh// statement defines a circle with integer label }(h/ statement defines a circle with integer label h j"_hhh!NhNubj)}(h *body_id*h]h/body_id}(hhh j>_ubah}(h]h]h]h]h]uhjh j"_ubh/
and radius }(h
and radius h j"_hhh!NhNubj)}(h*radius*h]h/radius}(hhh jQ_ubah}(h]h]h]h]h]uhjh j"_ubh/E, placed with its center at the origin (0,0) of the
unit. Modifiers: }(hE, placed with its center at the origin (0,0) of the
unit. Modifiers: h j"_hhh!NhNubj)}(h#*origin, rotate, chord, sides, com*h]h/!origin, rotate, chord, sides, com}(hhh jd_ubah}(h]h]h]h]h]uhjh j"_ubh/.}(hhh j"_hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j^hhubjH)}(h)hexprism body_id radius [modifier_list]h]h/)hexprism body_id radius [modifier_list]}(hhh j|_ubah}(h]h]h]h]h]j=j>uhjGh!h"hMh j^hhubhM)}(hX7The *hexprism* statement defines a standard hexagon with integer label
*body_id* and inscribed radius *radius*, placed with its center at the
origin (0,0) of the unit. A standard hexagon has vertices located on
north (top) and south (bottom) regions of the shape. Modifiers: *origin,
rotate, chord, sides, com.*h](h/The }(hThe h j_hhh!NhNubj)}(h
*hexprism*h]h/hexprism}(hhh j_ubah}(h]h]h]h]h]uhjh j_ubh/9 statement defines a standard hexagon with integer label
}(h9 statement defines a standard hexagon with integer label
h j_hhh!NhNubj)}(h *body_id*h]h/body_id}(hhh j_ubah}(h]h]h]h]h]uhjh j_ubh/ and inscribed radius }(h and inscribed radius h j_hhh!NhNubj)}(h*radius*h]h/radius}(hhh j_ubah}(h]h]h]h]h]uhjh j_ubh/, placed with its center at the
origin (0,0) of the unit. A standard hexagon has vertices located on
north (top) and south (bottom) regions of the shape. Modifiers: }(h, placed with its center at the
origin (0,0) of the unit. A standard hexagon has vertices located on
north (top) and south (bottom) regions of the shape. Modifiers: h j_hhh!NhNubj)}(h$*origin,
rotate, chord, sides, com.*h]h/"origin,
rotate, chord, sides, com.}(hhh j_ubah}(h]h]h]h]h]uhjh j_ubeh}(h]h]h]h]h]uhhLh!h"hMh j^hhubjH)}(h*rhexprism body_id radius [modifier_list]h]h/*rhexprism body_id radius [modifier_list]}(hhh j_ubah}(h]h]h]h]h]j=j>uhjGh!h"hMh j^hhubhM)}(hX4The *rhexprism* statement defines a rotated hexagon with integer label
*body_id* and inscribed radius *radius*, placed with its center at the
origin (0,0) of the unit. A rotated hexagon has vertices located on east
(right) and west (left) regions of the shape. Modifiers: *origin,
rotate, chord, sides, com.*h](h/The }(hThe h j_hhh!NhNubj)}(h*rhexprism*h]h/ rhexprism}(hhh j_ubah}(h]h]h]h]h]uhjh j_ubh/8 statement defines a rotated hexagon with integer label
}(h8 statement defines a rotated hexagon with integer label
h j_hhh!NhNubj)}(h *body_id*h]h/body_id}(hhh j
`ubah}(h]h]h]h]h]uhjh j_ubh/ and inscribed radius }(h and inscribed radius h j_hhh!NhNubj)}(h*radius*h]h/radius}(hhh j`ubah}(h]h]h]h]h]uhjh j_ubh/, placed with its center at the
origin (0,0) of the unit. A rotated hexagon has vertices located on east
(right) and west (left) regions of the shape. Modifiers: }(h, placed with its center at the
origin (0,0) of the unit. A rotated hexagon has vertices located on east
(right) and west (left) regions of the shape. Modifiers: h j_hhh!NhNubj)}(h$*origin,
rotate, chord, sides, com.*h]h/"origin,
rotate, chord, sides, com.}(hhh j0`ubah}(h]h]h]h]h]uhjh j_ubeh}(h]h]h]h]h]uhhLh!h"hMh j^hhubjH)}(h-wedge body_id xbase xpt ypt [modifier_list]h]h/-wedge body_id xbase xpt ypt [modifier_list]}(hhh jD`ubah}(h]h]h]h]h]j=j>uhjGh!h"hMh j^hhubhM)}(hThe *wedge* statement defines a triangle with integer label *body_id*
placed with a vertex at (0,0), a vertex at (x\ :sub:`base`,0), and a
vertex at (x\ :sub:`pt`,y\ :sub:`pt`). Modifiers: *origin, rotate, com.*h](h/The }(hThe h jR`hhh!NhNubj)}(h*wedge*h]h/wedge}(hhh j[`ubah}(h]h]h]h]h]uhjh jR`ubh/1 statement defines a triangle with integer label }(h1 statement defines a triangle with integer label h jR`hhh!NhNubj)}(h *body_id*h]h/body_id}(hhh jn`ubah}(h]h]h]h]h]uhjh jR`ubh/0
placed with a vertex at (0,0), a vertex at (x }(h0
placed with a vertex at (0,0), a vertex at (x\ h jR`hhh!NhNubj)}(h:sub:`base`h]h/base}(hhh j`ubah}(h]h]h]h]h]uhjh jR`ubh/,0), and a
vertex at (x }(h,0), and a
vertex at (x\ h jR`hhh!NhNubj)}(h :sub:`pt`h]h/pt}(hhh j`ubah}(h]h]h]h]h]uhjh jR`ubh/,y }(h,y\ h jR`hhh!NhNubj)}(h :sub:`pt`h]h/pt}(hhh j`ubah}(h]h]h]h]h]uhjh jR`ubh/). Modifiers: }(h). Modifiers: h jR`hhh!NhNubj)}(h*origin, rotate, com.*h]h/origin, rotate, com.}(hhh j`ubah}(h]h]h]h]h]uhjh jR`ubeh}(h]h]h]h]h]uhhLh!h"hMh j^hhubjH)}(h8array arrayid body_id place i j xij yij [modifier_list]h]h/8array arrayid body_id place i j xij yij [modifier_list]}(hhh j`ubah}(h]h]h]h]h]j=j>uhjGh!h"hMh j^hhubhM)}(hXThe *array* placement statement specifies the placement of an array with
identification number *arrayid* (defined in the array data block),
within shape *body_id*. If the *place* statement is used, the array
element located in row \ *i* (counted from the bottom) and column \ *j*
(counted from the left) is placed such that its origin is located at
spatial coordinate (*x\ ij*, *y\ ij*) of the unit in which it is placed.
Modifiers: *com*.h](h/The }(hThe h j`hhh!NhNubj)}(h*array*h]h/array}(hhh j`ubah}(h]h]h]h]h]uhjh j`ubh/T placement statement specifies the placement of an array with
identification number }(hT placement statement specifies the placement of an array with
identification number h j`hhh!NhNubj)}(h *arrayid*h]h/arrayid}(hhh j`ubah}(h]h]h]h]h]uhjh j`ubh/1 (defined in the array data block),
within shape }(h1 (defined in the array data block),
within shape h j`hhh!NhNubj)}(h *body_id*h]h/body_id}(hhh jaubah}(h]h]h]h]h]uhjh j`ubh/ . If the }(h . If the h j`hhh!NhNubj)}(h*place*h]h/place}(hhh jaubah}(h]h]h]h]h]uhjh j`ubh/8 statement is used, the array
element located in row }(h8 statement is used, the array
element located in row \ h j`hhh!NhNubj)}(h*i*h]h/i}(hhh j1aubah}(h]h]h]h]h]uhjh j`ubh/) (counted from the bottom) and column }(h) (counted from the bottom) and column \ h j`hhh!NhNubj)}(h*j*h]h/j}(hhh jDaubah}(h]h]h]h]h]uhjh j`ubh/Z
(counted from the left) is placed such that its origin is located at
spatial coordinate (}(hZ
(counted from the left) is placed such that its origin is located at
spatial coordinate (h j`hhh!NhNubj)}(h*x\ ij*h]h/x ij}(hhh jWaubah}(h]h]h]h]h]uhjh j`ubh/, }(h, h j`hhh!NhNubj)}(h*y\ ij*h]h/y ij}(hhh jjaubah}(h]h]h]h]h]uhjh j`ubh/0) of the unit in which it is placed.
Modifiers: }(h0) of the unit in which it is placed.
Modifiers: h j`hhh!NhNubj)}(h*com*h]h/com}(hhh j}aubah}(h]h]h]h]h]uhjh j`ubh/.}(hhh j`hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j^hhubjH)}(hhole unit_id [modifier_list]h]h/hole unit_id [modifier_list]}(hhh jaubah}(h]h]h]h]h]j=j>uhjGh!h"hMh j^hhubhM)}(hXThe *hole* statement is used to place a different unit identified by
label *unit_id* within the current unit. The origin of the unit being
placed will be located at the origin of the current unit but can be
repositioned using the *origin* modifier. Modifiers: *origin, rotate,
com*.h](h/The }(hThe h jahhh!NhNubj)}(h*hole*h]h/hole}(hhh jaubah}(h]h]h]h]h]uhjh jaubh/A statement is used to place a different unit identified by
label }(hA statement is used to place a different unit identified by
label h jahhh!NhNubj)}(h *unit_id*h]h/unit_id}(hhh jaubah}(h]h]h]h]h]uhjh jaubh/ within the current unit. The origin of the unit being
placed will be located at the origin of the current unit but can be
repositioned using the }(h within the current unit. The origin of the unit being
placed will be located at the origin of the current unit but can be
repositioned using the h jahhh!NhNubj)}(h*origin*h]h/origin}(hhh jaubah}(h]h]h]h]h]uhjh jaubh/ modifier. Modifiers: }(h modifier. Modifiers: h jahhh!NhNubj)}(h*origin, rotate,
com*h]h/origin, rotate,
com}(hhh jaubah}(h]h]h]h]h]uhjh jaubh/.}(hhh jahhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j^hhubjH)}(h3media materialid bias_placeholder reg_def_vectorh]h/3media materialid bias_placeholder reg_def_vector}(hhh jaubah}(h]h]h]h]h]j=j>uhjGh!h"hMh j^hhubhM)}(hXThe *media* statement assigns material properties associated with
mixture index *materialid* to a shape region defined within a unit. The
*bias_placeholder* term is not currently used but is retained for
consistency with KENO-VI; typically it is assigned a value of 1.
*reg_def_vector* is the region definition vector and assigns the mixture
placement relative to shapes within the unit. If the index is positive,
the shape region is included in the material assignment; if negative, it
is excluded. Modifiers: none.h](h/The }(hThe h jbhhh!NhNubj)}(h*media*h]h/media}(hhh jbubah}(h]h]h]h]h]uhjh jbubh/E statement assigns material properties associated with
mixture index }(hE statement assigns material properties associated with
mixture index h jbhhh!NhNubj)}(h*materialid*h]h/
materialid}(hhh j'bubah}(h]h]h]h]h]uhjh jbubh/. to a shape region defined within a unit. The
}(h. to a shape region defined within a unit. The
h jbhhh!NhNubj)}(h*bias_placeholder*h]h/bias_placeholder}(hhh j:bubah}(h]h]h]h]h]uhjh jbubh/q term is not currently used but is retained for
consistency with KENO-VI; typically it is assigned a value of 1.
}(hq term is not currently used but is retained for
consistency with KENO-VI; typically it is assigned a value of 1.
h jbhhh!NhNubj)}(h*reg_def_vector*h]h/reg_def_vector}(hhh jMbubah}(h]h]h]h]h]uhjh jbubh/ is the region definition vector and assigns the mixture
placement relative to shapes within the unit. If the index is positive,
the shape region is included in the material assignment; if negative, it
is excluded. Modifiers: none.}(h is the region definition vector and assigns the mixture
placement relative to shapes within the unit. If the index is positive,
the shape region is included in the material assignment; if negative, it
is excluded. Modifiers: none.h jbhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j^hhubjH)}(h6boundary body_id [x-discretization y-discretization]h]h/6boundary body_id [x-discretization y-discretization]}(hhh jfbubah}(h]h]h]h]h]j=j>uhjGh!h"hMh j^hhubhM)}(hXThe *boundary* statement is used to define the outer boundary of the
unit, corresponding to the outer bounds of the shape *body_id* within
the unit. This shape must exist and must contain all other bodies
associated with the unit. The *x-discretization* and *y-discretization*
terms are integers (≥2) that specify the number of cells to be placed in
the unit in the x-direction and y-direction, respectively. A grid
specification is required for the global unit but is optional for other
units. Modifiers: none.h](h/The }(hThe h jtbhhh!NhNubj)}(h
*boundary*h]h/boundary}(hhh j}bubah}(h]h]h]h]h]uhjh jtbubh/l statement is used to define the outer boundary of the
unit, corresponding to the outer bounds of the shape }(hl statement is used to define the outer boundary of the
unit, corresponding to the outer bounds of the shape h jtbhhh!NhNubj)}(h *body_id*h]h/body_id}(hhh jbubah}(h]h]h]h]h]uhjh jtbubh/h within
the unit. This shape must exist and must contain all other bodies
associated with the unit. The }(hh within
the unit. This shape must exist and must contain all other bodies
associated with the unit. The h jtbhhh!NhNubj)}(h*x-discretization*h]h/x-discretization}(hhh jbubah}(h]h]h]h]h]uhjh jtbubh/ and }(h and h jtbhhh!NhNubj)}(h*y-discretization*h]h/y-discretization}(hhh jbubah}(h]h]h]h]h]uhjh jtbubh/
terms are integers (≥2) that specify the number of cells to be placed in
the unit in the x-direction and y-direction, respectively. A grid
specification is required for the global unit but is optional for other
units. Modifiers: none.}(h
terms are integers (≥2) that specify the number of cells to be placed in
the unit in the x-direction and y-direction, respectively. A grid
specification is required for the global unit but is optional for other
units. Modifiers: none.h jtbhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j^hhubh)}(h.. _9-2-3-6-5-2:h]h}(h]h]h]h]h]hid90uhh
hMh j^hhh!h"ubeh}(h](unit-definition-statementsj^eh]h](unit definition statements9-2-3-6-5-1eh]h]uhh#h j]hhh!h"hMj}jbj^sj}j^j^subh$)}(hhh](h))}(hGeometry modifiersh]h/Geometry modifiers}(hjbh jbhhh!NhNubah}(h]h]h]h]h]uhh(h jbhhh!h"hMubjH)}(horigin x=xnew y=ynewh]h/origin x=xnew y=ynew}(hhh jbubah}(h]h]h]h]h]j=j>uhjGh!h"hMh jbhhubhM)}(hUsed to relocate the origin of cylinders, hexprisms, rhexprisms, and
holes to new co-ordinate (x\ :sub:`new`, y\ :sub:`new`). The default (if
not specified) is to place the origin of the body at (0, 0).h](h/bUsed to relocate the origin of cylinders, hexprisms, rhexprisms, and
holes to new co-ordinate (x }(hbUsed to relocate the origin of cylinders, hexprisms, rhexprisms, and
holes to new co-ordinate (x\ h jchhh!NhNubj)}(h
:sub:`new`h]h/new}(hhh j
cubah}(h]h]h]h]h]uhjh jcubh/, y }(h, y\ h jchhh!NhNubj)}(h
:sub:`new`h]h/new}(hhh j cubah}(h]h]h]h]h]uhjh jcubh/O). The default (if
not specified) is to place the origin of the body at (0, 0).}(hO). The default (if
not specified) is to place the origin of the body at (0, 0).h jchhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jbhhubjH)}(hrotate a1=Ah]h/rotate a1=A}(hhh j9cubah}(h]h]h]h]h]j=j>uhjGh!h"hMh jbhhubhM)}(hCauses a body to be rotated by an angle of *A* degrees
(counterclockwise) around its origin. It can be applied to holes and all
basic shapes; the default is 0 degrees.h](h/+Causes a body to be rotated by an angle of }(h+Causes a body to be rotated by an angle of h jGchhh!NhNubj)}(h*A*h]h/A}(hhh jPcubah}(h]h]h]h]h]uhjh jGcubh/{ degrees
(counterclockwise) around its origin. It can be applied to holes and all
basic shapes; the default is 0 degrees.}(h{ degrees
(counterclockwise) around its origin. It can be applied to holes and all
basic shapes; the default is 0 degrees.h jGchhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jbhhubjH)}(h#chord ±x=xplane
chord ±y=yplaneh]h/#chord ±x=xplane
chord ±y=yplane}(hhh jicubah}(h]h]h]h]h]j=j>uhjGh!h"hM h jbhhubhM)}(hXChords are used to truncate a shape at the line x=\ *chord* (or
y=\ *chord*). Multiple chord commands are allowed, but only one line
(either in x- or y-direction) is specified for each. If the negative
keyword ‘–x’ (or ‘–y’) appears, then the part of the shape to the left
of (below) the chord cut is retained. Similarly, if the positive keyword
(‘+x’ or ‘+y’) is used, then the portion of the shape to the right of or
above the chord is retained. Chords may be applied to cylinders,
hexprisms, and rhexprisms only.h](h/4Chords are used to truncate a shape at the line x= }(h4Chords are used to truncate a shape at the line x=\ h jwchhh!NhNubj)}(h*chord*h]h/chord}(hhh jcubah}(h]h]h]h]h]uhjh jwcubh/ (or
y= }(h (or
y=\ h jwchhh!NhNubj)}(h*chord*h]h/chord}(hhh jcubah}(h]h]h]h]h]uhjh jwcubh/X). Multiple chord commands are allowed, but only one line
(either in x- or y-direction) is specified for each. If the negative
keyword ‘–x’ (or ‘–y’) appears, then the part of the shape to the left
of (below) the chord cut is retained. Similarly, if the positive keyword
(‘+x’ or ‘+y’) is used, then the portion of the shape to the right of or
above the chord is retained. Chords may be applied to cylinders,
hexprisms, and rhexprisms only.}(hX). Multiple chord commands are allowed, but only one line
(either in x- or y-direction) is specified for each. If the negative
keyword ‘–x’ (or ‘–y’) appears, then the part of the shape to the left
of (below) the chord cut is retained. Similarly, if the positive keyword
(‘+x’ or ‘+y’) is used, then the portion of the shape to the right of or
above the chord is retained. Chords may be applied to cylinders,
hexprisms, and rhexprisms only.h jwchhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jbhhubjH)}(hsides=Nh]h/sides=N}(hhh jcubah}(h]h]h]h]h]j=j>uhjGh!h"hMh jbhhubhM)}(hXhFor use with the cylinder statement, the *sides* modifier specifies the
number of sides on the regular polygon used to approximate the cylinder.
Its default is N = 12. The radius of the polygon is adjusted such that
the area of the polygon matches the area of the cylinder it is
approximating. The *sides* modifier is unique to NEWT and is not used by
KENO-VI.h](h/)For use with the cylinder statement, the }(h)For use with the cylinder statement, the h jchhh!NhNubj)}(h*sides*h]h/sides}(hhh jcubah}(h]h]h]h]h]uhjh jcubh/ modifier specifies the
number of sides on the regular polygon used to approximate the cylinder.
Its default is N = 12. The radius of the polygon is adjusted such that
the area of the polygon matches the area of the cylinder it is
approximating. The }(h modifier specifies the
number of sides on the regular polygon used to approximate the cylinder.
Its default is N = 12. The radius of the polygon is adjusted such that
the area of the polygon matches the area of the cylinder it is
approximating. The h jchhh!NhNubj)}(h*sides*h]h/sides}(hhh jcubah}(h]h]h]h]h]uhjh jcubh/7 modifier is unique to NEWT and is not used by
KENO-VI.}(h7 modifier is unique to NEWT and is not used by
KENO-VI.h jchhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jbhhubh)}(h.. _9-2-3-7:h]h}(h]h]h]h]h]hid91uhh
hM h jbhhh!h"ubeh}(h](geometry-modifiersjbeh]h](geometry modifiers9-2-3-6-5-2eh]h]uhh#h j]hhh!h"hMj}jdjbsj}jbjbsubeh}(h]("summary-of-geometry-specificationsj]eh]h]("summary of geometry specifications 9-2-3-6-5eh]h]uhh#h j>hhh!h"hMj}jdj]sj}j]j]subeh}(h](geometry-blockj>eh]h](geometry block9-2-3-6eh]h]uhh#h jhhh!h"hMj}jdj>sj}j>j>subh$)}(hhh](h))}(hBoundary conditionsh]h/Boundary conditions}(hj dh jdhhh!NhNubah}(h]h]h]h]h]uhh(h jdhhh!h"hM#ubhM)}(hXThe *geometry data* block is generally followed by the *bounds* data
block, in which boundary conditions for the sides of the bounding shape
in the global array are specified. NEWT supports the use of cuboid,
hexprism, and wedge shapes to define outer boundaries. This results in
the need to specify up to 6 surface boundaries, on up to 8 spatial
orientations. In other words, a cuboid will have boundaries on +x, ‑x,
+y, and –y faces. A regular hexprism will have boundaries on +x and -x
faces; it will also have boundaries on the four sloped sides of the hex.
In order to identify the sense of sides for specification of boundary
conditions, NEWT applies an eight-point compass nomenclature. The four
permitted rectangular boundary surfaces are identified as +x, -x, +y,
and –y, corresponding to east (E), west (W), north (N), and south (S)
faces, as illustrated in :numref:`fig9-2-32` Sloped (non-rectangular) surfaces
are identified as +x+y, +x‑y, -x-y, and –x+y, for northeast (NE),
southeast (SE), southwest (SW), and northwest (NW) surfaces. No
assumptions are made on the slope of the various non-rectangular
surfaces; for the bodies available within NEWT, it is not possible to
have more than one surface in each octant.h](h/The }(hThe h j,dhhh!NhNubj)}(h*geometry data*h]h/
geometry data}(hhh j5dubah}(h]h]h]h]h]uhjh j,dubh/$ block is generally followed by the }(h$ block is generally followed by the h j,dhhh!NhNubj)}(h*bounds*h]h/bounds}(hhh jHdubah}(h]h]h]h]h]uhjh j,dubh/X, data
block, in which boundary conditions for the sides of the bounding shape
in the global array are specified. NEWT supports the use of cuboid,
hexprism, and wedge shapes to define outer boundaries. This results in
the need to specify up to 6 surface boundaries, on up to 8 spatial
orientations. In other words, a cuboid will have boundaries on +x, ‑x,
+y, and –y faces. A regular hexprism will have boundaries on +x and -x
faces; it will also have boundaries on the four sloped sides of the hex.
In order to identify the sense of sides for specification of boundary
conditions, NEWT applies an eight-point compass nomenclature. The four
permitted rectangular boundary surfaces are identified as +x, -x, +y,
and –y, corresponding to east (E), west (W), north (N), and south (S)
faces, as illustrated in }(hX, data
block, in which boundary conditions for the sides of the bounding shape
in the global array are specified. NEWT supports the use of cuboid,
hexprism, and wedge shapes to define outer boundaries. This results in
the need to specify up to 6 surface boundaries, on up to 8 spatial
orientations. In other words, a cuboid will have boundaries on +x, ‑x,
+y, and –y faces. A regular hexprism will have boundaries on +x and -x
faces; it will also have boundaries on the four sloped sides of the hex.
In order to identify the sense of sides for specification of boundary
conditions, NEWT applies an eight-point compass nomenclature. The four
permitted rectangular boundary surfaces are identified as +x, -x, +y,
and –y, corresponding to east (E), west (W), north (N), and south (S)
faces, as illustrated in h j,dhhh!NhNubj)}(h:numref:`fig9-2-32`h]jM)}(hj]dh]h/ fig9-2-32}(hhh j_dubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh j[dubah}(h]h]h]h]h]refdochj refdomainjidreftypenumrefrefexplicitrefwarnjW fig9-2-32uhjh!h"hM%h j,dubh/XZ Sloped (non-rectangular) surfaces
are identified as +x+y, +x‑y, -x-y, and –x+y, for northeast (NE),
southeast (SE), southwest (SW), and northwest (NW) surfaces. No
assumptions are made on the slope of the various non-rectangular
surfaces; for the bodies available within NEWT, it is not possible to
have more than one surface in each octant.}(hXZ Sloped (non-rectangular) surfaces
are identified as +x+y, +x‑y, -x-y, and –x+y, for northeast (NE),
southeast (SE), southwest (SW), and northwest (NW) surfaces. No
assumptions are made on the slope of the various non-rectangular
surfaces; for the bodies available within NEWT, it is not possible to
have more than one surface in each octant.h j,dhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM%h jdhhubh)}(h.. _fig9-2-32:h]h}(h]h]h]h]h]h fig9-2-32uhh
hM8h jdhhh!h"ubj)}(hhh](j)}(h{.. figure:: figs/NEWT/fig32.png
:align: center
:width: 400
Two-dimensional boundary condition surface orientations.
h]h}(h]h]h]h]h]width400urifigs/NEWT/fig32.pngj*}j,jdsuhjh jdh!h"hM=ubj.)}(h8Two-dimensional boundary condition surface orientations.h]h/8Two-dimensional boundary condition surface orientations.}(hjdh jdubah}(h]h]h]h]h]uhj-h!h"hM=h jdubeh}(h](id190jdeh]h] fig9-2-32ah]h]jEcenteruhjhM=h jdhhh!h"j}jdjdsj}jdjdsubhM)}(hCurrently, full specification of boundary conditions is permitted only
when the boundary body for the global unit is a cuboid. Only white and
vacuum boundary conditions are permitted on non-rectangular surfaces.h]h/Currently, full specification of boundary conditions is permitted only
when the boundary body for the global unit is a cuboid. Only white and
vacuum boundary conditions are permitted on non-rectangular surfaces.}(hjdh jdhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM?h jdhhubhM)}(hBoundary conditions therefore may only be specified for the ±x and
±y faces of a boundary cuboid. Four boundary conditions are currently
supported:h]h/Boundary conditions therefore may only be specified for the ±x and
±y faces of a boundary cuboid. Four boundary conditions are currently
supported:}(hjdh jdhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMCh jdhhubjP)}(hhh]h;)}(hhh](h@)}(hreflective (default),
h]hM)}(hreflective (default),h]h/reflective (default),}(hjdh jdubah}(h]h]h]h]h]uhhLh!h"hMGh jdubah}(h]h]h]h]h]uhh?h jdubh@)}(hwhite,
h]hM)}(hwhite,h]h/white,}(hjdh jdubah}(h]h]h]h]h]uhhLh!h"hMIh jdubah}(h]h]h]h]h]uhh?h jdubh@)}(hvacuum, and
h]hM)}(hvacuum, andh]h/vacuum, and}(hjeh jeubah}(h]h]h]h]h]uhhLh!h"hMKh jeubah}(h]h]h]h]h]uhh?h jdubh@)}(h
periodic.
h]hM)}(h periodic.h]h/ periodic.}(hj,eh j*eubah}(h]h]h]h]h]uhhLh!h"hMMh j&eubah}(h]h]h]h]h]uhh?h jdubeh}(h]h]h]h]h]h~j hhhhuhh:h jdubah}(h]h]h]h]h]uhjOh jdhhh!NhNubhM)}(hAlbedo boundary conditions are not yet supported but will be available
in a future release. Additional information on the meaning of each
boundary condition type is provided in the following section.h]h/Albedo boundary conditions are not yet supported but will be available
in a future release. Additional information on the meaning of each
boundary condition type is provided in the following section.}(hjLeh jJehhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMOh jdhhubh)}(h.. _9-2-3-7-1:h]h}(h]h]h]h]h]hid92uhh
hMSh jdhhh!h"ubh$)}(hhh](h))}(h Boundary conditions descriptionsh]h/ Boundary conditions descriptions}(hjheh jfehhh!NhNubah}(h]h]h]h]h]uhh(h jcehhh!h"hMVubhM)}(hXMBoundary conditions are mathematical approximations used to describe the
behavior of neutrons when they cross a problem boundary. Typically,
transport methods provide for reflective (or mirror), white, vacuum, or
periodic boundary conditions. The following subsections describe and
illustrate these four types of boundary conditions.h]h/XMBoundary conditions are mathematical approximations used to describe the
behavior of neutrons when they cross a problem boundary. Typically,
transport methods provide for reflective (or mirror), white, vacuum, or
periodic boundary conditions. The following subsections describe and
illustrate these four types of boundary conditions.}(hjveh jtehhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMXh jcehhubh)}(h.. _9-2-3-7-1-1:h]h}(h]h]h]h]h]hid93uhh
hM^h jcehhh!h"ubh$)}(hhh](h))}(hReflective boundary conditionh]h/Reflective boundary condition}(hjeh jehhh!NhNubah}(h]h]h]h]h]uhh(h jehhh!h"hMaubhM)}(hXFor the reflective boundary condition, the incoming angular flux is set
equal to the outgoing angular flux in the direction corresponding to
mirror or specular reflection. As shown in :numref:`fig9-2-33`, a given
quantity of neutrons leaving a boundary (dotted line) in a particular
direction will be returned (solid line of same color) to the system with
the same quantity but at a mirrored angle to the initial leakage
direction.h](h/For the reflective boundary condition, the incoming angular flux is set
equal to the outgoing angular flux in the direction corresponding to
mirror or specular reflection. As shown in }(hFor the reflective boundary condition, the incoming angular flux is set
equal to the outgoing angular flux in the direction corresponding to
mirror or specular reflection. As shown in h jehhh!NhNubj)}(h:numref:`fig9-2-33`h]jM)}(hjeh]h/ fig9-2-33}(hhh jeubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jeubah}(h]h]h]h]h]refdochj refdomainjereftypenumrefrefexplicitrefwarnjW fig9-2-33uhjh!h"hMch jeubh/, a given
quantity of neutrons leaving a boundary (dotted line) in a particular
direction will be returned (solid line of same color) to the system with
the same quantity but at a mirrored angle to the initial leakage
direction.}(h, a given
quantity of neutrons leaving a boundary (dotted line) in a particular
direction will be returned (solid line of same color) to the system with
the same quantity but at a mirrored angle to the initial leakage
direction.h jehhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMch jehhubh note)}(hXIn the following figures, a dashed arrow indicates neutrons
leaving the system while a solid arrow represents those returning to the
system. The length of the arrow is proportional to the number of
neutrons; therefore, longer arrows represent more neutrons than do
shorter arrows.h]hM)}(hXIn the following figures, a dashed arrow indicates neutrons
leaving the system while a solid arrow represents those returning to the
system. The length of the arrow is proportional to the number of
neutrons; therefore, longer arrows represent more neutrons than do
shorter arrows.h]h/XIn the following figures, a dashed arrow indicates neutrons
leaving the system while a solid arrow represents those returning to the
system. The length of the arrow is proportional to the number of
neutrons; therefore, longer arrows represent more neutrons than do
shorter arrows.}(hjeh jeubah}(h]h]h]h]h]uhhLh!h"hMkh jeubah}(h]h]h]h]h]uhjeh jehhh!h"hNubh)}(h.. _fig9-2-33:h]h}(h]h]h]h]h]h fig9-2-33uhh
hMqh jehhh!h"ubj)}(hhh](j)}(ha.. figure:: figs/NEWT/fig33.png
:align: center
:width: 500
Reflective boundary condition.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig33.pngj*}j,jfsuhjh jeh!h"hMvubj.)}(hReflective boundary condition.h]h/Reflective boundary condition.}(hjfh j fubah}(h]h]h]h]h]uhj-h!h"hMvh jeubeh}(h](id191jeeh]h] fig9-2-33ah]h]jEcenteruhjhMvh jehhh!h"j}jfjesj}jejesubh)}(h.. _9-2-3-7-1-2:h]h}(h]h]h]h]h]hid94uhh
hMxh jehhh!h"ubeh}(h](reflective-boundary-conditionjeeh]h](reflective boundary condition9-2-3-7-1-1eh]h]uhh#h jcehhh!h"hMaj}j3fjesj}jejesubh$)}(hhh](h))}(hWhite boundary conditionh]h/White boundary condition}(hj=fh j;fhhh!NhNubah}(h]h]h]h]h]uhh(h j8fhhh!h"hM{ubhM)}(hFor the white boundary condition, the incoming angular fluxes are each
set equal to a single value chosen such that the net flow across the
boundary is zero. The white boundary provides isotropic return (solid
lines) at a boundary (:numref:`fig9-2-34`).h](h/For the white boundary condition, the incoming angular fluxes are each
set equal to a single value chosen such that the net flow across the
boundary is zero. The white boundary provides isotropic return (solid
lines) at a boundary (}(hFor the white boundary condition, the incoming angular fluxes are each
set equal to a single value chosen such that the net flow across the
boundary is zero. The white boundary provides isotropic return (solid
lines) at a boundary (h jIfhhh!NhNubj)}(h:numref:`fig9-2-34`h]jM)}(hjTfh]h/ fig9-2-34}(hhh jVfubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jRfubah}(h]h]h]h]h]refdochj refdomainj`freftypenumrefrefexplicitrefwarnjW fig9-2-34uhjh!h"hM}h jIfubh/).}(h).h jIfhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM}h j8fhhubh)}(h.. _fig9-2-34:h]h}(h]h]h]h]h]h fig9-2-34uhh
hMh j8fhhh!h"ubj)}(hhh](j)}(h\.. figure:: figs/NEWT/fig34.png
:align: center
:width: 500
White boundary condition.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig34.pngj*}j,jfsuhjh jfh!h"hMubj.)}(hWhite boundary condition.h]h/White boundary condition.}(hjfh jfubah}(h]h]h]h]h]uhj-h!h"hMh jfubeh}(h](id192jfeh]h] fig9-2-34ah]h]jEcenteruhjhMh j8fhhh!h"j}jfj}fsj}jfj}fsubh)}(h.. _9-2-3-7-1-3:h]h}(h]h]h]h]h]hid95uhh
hMh j8fhhh!h"ubeh}(h](white-boundary-conditionj,feh]h](white boundary condition9-2-3-7-1-2eh]h]uhh#h jcehhh!h"hM{j}jfj"fsj}j,fj"fsubh$)}(hhh](h))}(hVacuum boundary conditionh]h/Vacuum boundary condition}(hjfh jfhhh!NhNubah}(h]h]h]h]h]uhh(h jfhhh!h"hMubhM)}(hA vacuum boundary condition means that no neutrons will reenter the
boundary. Thus, any neutron exiting the system through a boundary with a
vacuum boundary condition is permanently lost to the system. This
condition is illustrated in :numref:`fig9-2-35`.h](h/A vacuum boundary condition means that no neutrons will reenter the
boundary. Thus, any neutron exiting the system through a boundary with a
vacuum boundary condition is permanently lost to the system. This
condition is illustrated in }(hA vacuum boundary condition means that no neutrons will reenter the
boundary. Thus, any neutron exiting the system through a boundary with a
vacuum boundary condition is permanently lost to the system. This
condition is illustrated in h jfhhh!NhNubj)}(h:numref:`fig9-2-35`h]jM)}(hjfh]h/ fig9-2-35}(hhh jfubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jfubah}(h]h]h]h]h]refdochj refdomainjfreftypenumrefrefexplicitrefwarnjW fig9-2-35uhjh!h"hMh jfubh/.}(hhh jfhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jfhhubh)}(h.. _fig9-2-35:h]h}(h]h]h]h]h]h fig9-2-35uhh
hMh jfhhh!h"ubj)}(hhh](j)}(h].. figure:: figs/NEWT/fig35.png
:align: center
:width: 500
Vacuum boundary condition.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig35.pngj*}j,j(gsuhjh jgh!h"hMubj.)}(hVacuum boundary condition.h]h/Vacuum boundary condition.}(hj,gh j*gubah}(h]h]h]h]h]uhj-h!h"hMh jgubeh}(h](id193jgeh]h] fig9-2-35ah]h]jEcenteruhjhMh jfhhh!h"j}j=gj
gsj}jgj
gsubh)}(h.. _9-2-3-7-1-4:h]h}(h]h]h]h]h]hid96uhh
hMh jfhhh!h"ubeh}(h](vacuum-boundary-conditionjfeh]h](vacuum boundary condition9-2-3-7-1-3eh]h]uhh#h jcehhh!h"hMj}jTgjfsj}jfjfsubh$)}(hhh](h))}(hPeriodic boundary conditionh]h/Periodic boundary condition}(hj^gh j\ghhh!NhNubah}(h]h]h]h]h]uhh(h jYghhh!h"hMubhM)}(hXFor the periodic boundary condition, the incoming angular flux on a
boundary is set equal to the outgoing angular flux on the opposite
boundary. :numref:`fig9-2-36` shows the leakage leaving each boundary (dotted
lines) being returned at the same quantity and angle on the opposite
boundary (solid line of same color). When the periodic boundary
condition is used, it must be applied to both opposing boundaries.h](h/For the periodic boundary condition, the incoming angular flux on a
boundary is set equal to the outgoing angular flux on the opposite
boundary. }(hFor the periodic boundary condition, the incoming angular flux on a
boundary is set equal to the outgoing angular flux on the opposite
boundary. h jjghhh!NhNubj)}(h:numref:`fig9-2-36`h]jM)}(hjugh]h/ fig9-2-36}(hhh jwgubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jsgubah}(h]h]h]h]h]refdochj refdomainjgreftypenumrefrefexplicitrefwarnjW fig9-2-36uhjh!h"hMh jjgubh/ shows the leakage leaving each boundary (dotted
lines) being returned at the same quantity and angle on the opposite
boundary (solid line of same color). When the periodic boundary
condition is used, it must be applied to both opposing boundaries.}(h shows the leakage leaving each boundary (dotted
lines) being returned at the same quantity and angle on the opposite
boundary (solid line of same color). When the periodic boundary
condition is used, it must be applied to both opposing boundaries.h jjghhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jYghhubh)}(h.. _fig9-2-36:h]h}(h]h]h]h]h]h fig9-2-36uhh
hMh jYghhh!h"ubj)}(hhh](j)}(h_.. figure:: figs/NEWT/fig36.png
:align: center
:width: 500
Periodic boundary condition.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig36.pngj*}j,jgsuhjh jgh!h"hMubj.)}(hPeriodic boundary condition.h]h/Periodic boundary condition.}(hjgh jgubah}(h]h]h]h]h]uhj-h!h"hMh jgubeh}(h](id194jgeh]h] fig9-2-36ah]h]jEcenteruhjhMh jYghhh!h"j}jgjgsj}jgjgsubh)}(h.. _9-2-3-7-2:h]h}(h]h]h]h]h]hid97uhh
hMh jYghhh!h"ubeh}(h](periodic-boundary-conditionjMgeh]h](periodic boundary condition9-2-3-7-1-4eh]h]uhh#h jcehhh!h"hMj}jgjCgsj}jMgjCgsubeh}(h]( boundary-conditions-descriptionsjbeeh]h]( boundary conditions descriptions 9-2-3-7-1eh]h]uhh#h jdhhh!h"hMVj}jgjXesj}jbejXesubh$)}(hhh](h))}(h Boundary condition specificationh]h/ Boundary condition specification}(hjgh jghhh!NhNubah}(h]h]h]h]h]uhh(h jghhh!h"hMubhM)}(hHThe standard format for boundary condition specifications is as follows:h]h/HThe standard format for boundary condition specifications is as follows:}(hjhh jhhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jghhubjH)}(hread bounds
-x=west_BC +x=east_BC -y=south_BC +y=north_BC
+x+y=northeast_BC +x-y=southeast_BC
-x+y=northwest_BC -x-y=southwest_BC
end boundsh]h/read bounds
-x=west_BC +x=east_BC -y=south_BC +y=north_BC
+x+y=northeast_BC +x-y=southeast_BC
-x+y=northwest_BC -x-y=southwest_BC
end bounds}(hhh jhubah}(h]h]h]h]h]j=j>uhjGh!h"hMh jghhubhM)}(hXwhere *west_BC, east_BC, south_BC, north_BC, northeast_BC, southeast_BC,
northwest_BC, southwest_BC* are each one of the eight possible boundary
condition options. The name of the boundary condition requires only the
number of leading characters required to make the name unique. For this
set, the first letter is sufficient; that is, +x=v, +x=vac +x=vacu, and
+x=vacuum are all equivalent and specify a vacuum (zero return) boundary
condition on the right side of the global cuboid.h](h/where }(hwhere h j"hhhh!NhNubj)}(h^*west_BC, east_BC, south_BC, north_BC, northeast_BC, southeast_BC,
northwest_BC, southwest_BC*h]h/\west_BC, east_BC, south_BC, north_BC, northeast_BC, southeast_BC,
northwest_BC, southwest_BC}(hhh j+hubah}(h]h]h]h]h]uhjh j"hubh/X are each one of the eight possible boundary
condition options. The name of the boundary condition requires only the
number of leading characters required to make the name unique. For this
set, the first letter is sufficient; that is, +x=v, +x=vac +x=vacu, and
+x=vacuum are all equivalent and specify a vacuum (zero return) boundary
condition on the right side of the global cuboid.}(hX are each one of the eight possible boundary
condition options. The name of the boundary condition requires only the
number of leading characters required to make the name unique. For this
set, the first letter is sufficient; that is, +x=v, +x=vac +x=vacu, and
+x=vacuum are all equivalent and specify a vacuum (zero return) boundary
condition on the right side of the global cuboid.h j"hhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jghhubhM)}(hIn keeping with KENO-VI, multiple shortcuts exist to simplify the
specification. For example, a single boundary condition can be assigned
to all four sides simultaneously with the *all=* specifier:h](h/In keeping with KENO-VI, multiple shortcuts exist to simplify the
specification. For example, a single boundary condition can be assigned
to all four sides simultaneously with the }(hIn keeping with KENO-VI, multiple shortcuts exist to simplify the
specification. For example, a single boundary condition can be assigned
to all four sides simultaneously with the h jDhhhh!NhNubj)}(h*all=*h]h/all=}(hhh jMhubah}(h]h]h]h]h]uhjh jDhubh/ specifier:}(h specifier:h jDhhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jghhubjH)}(hread bounds
all=refl
end boundsh]h/read bounds
all=refl
end bounds}(hhh jfhubah}(h]h]h]h]h]j=j>uhjGh!h"hMh jghhubhM)}(hzAll KENO-VI boundary face keywords that do not reference the z-dimension
are allowed and are listed in :numref:`tab9-2-1`.h](h/gAll KENO-VI boundary face keywords that do not reference the z-dimension
are allowed and are listed in }(hgAll KENO-VI boundary face keywords that do not reference the z-dimension
are allowed and are listed in h jthhhh!NhNubj)}(h:numref:`tab9-2-1`h]jM)}(hjhh]h/tab9-2-1}(hhh jhubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh j}hubah}(h]h]h]h]h]refdochj refdomainjhreftypenumrefrefexplicitrefwarnjWtab9-2-1uhjh!h"hMh jthubh/.}(hhh jthhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jghhubh)}(h
.. _tab9-2-1:h]h}(h]h]h]h]h]htab9-2-1uhh
hMh jghhh!h"ubj)}(hhh](h))}(h/Boundary condition specifiers accepted by NEWT.h]h//Boundary condition specifiers accepted by NEWT.}(hjhh jhubah}(h]h]h]h]h]uhh(h!h"hMh jhubj)}(hhh](j)}(hhh]h}(h]h]h]h]h]colwidthKuhjh jhubj)}(hhh]h}(h]h]h]h]h]colwidthK!uhjh jhubh thead)}(hhh]j)}(hhh](j)}(hhh]hM)}(h**Keyword**h]h)}(hjhh]h/Keyword}(hhh jhubah}(h]h]h]h]h]uhhh jhubah}(h]h]h]h]h]uhhLh!h"hMh jhubah}(h]h]h]h]h]uhjh jhubj)}(hhh]hM)}(h**Boundary edge**h]h)}(hjih]h/
Boundary edge}(hhh j iubah}(h]h]h]h]h]uhhh jiubah}(h]h]h]h]h]uhhLh!h"hMh jiubah}(h]h]h]h]h]uhjh jhubeh}(h]h]h]h]h]uhjh jhubah}(h]h]h]h]h]uhjhh jhubj)}(hhh](j)}(hhh](j)}(hhh]hM)}(h+x, +xbh]h/+x, +xb}(hj9ih j7iubah}(h]h]h]h]h]uhhLh!h"hMh j4iubah}(h]h]h]h]h]uhjh j1iubj)}(hhh]hM)}(hEast (right)h]h/East (right)}(hjPih jNiubah}(h]h]h]h]h]uhhLh!h"hMh jKiubah}(h]h]h]h]h]uhjh j1iubeh}(h]h]h]h]h]uhjh j.iubj)}(hhh](j)}(hhh]hM)}(h-x, -xbh]h/-x, -xb}(hjpih jniubah}(h]h]h]h]h]uhhLh!h"hMh jkiubah}(h]h]h]h]h]uhjh jhiubj)}(hhh]hM)}(hWest (left)h]h/West (left)}(hjih jiubah}(h]h]h]h]h]uhhLh!h"hMh jiubah}(h]h]h]h]h]uhjh jhiubeh}(h]h]h]h]h]uhjh j.iubj)}(hhh](j)}(hhh]hM)}(h+y, +ybh]h/+y, +yb}(hjih jiubah}(h]h]h]h]h]uhhLh!h"hMh jiubah}(h]h]h]h]h]uhjh jiubj)}(hhh]hM)}(hNorth (top)h]h/North (top)}(hjih jiubah}(h]h]h]h]h]uhhLh!h"hMh jiubah}(h]h]h]h]h]uhjh jiubeh}(h]h]h]h]h]uhjh j.iubj)}(hhh](j)}(hhh]hM)}(h-y, -ybh]h/-y, -yb}(hjih jiubah}(h]h]h]h]h]uhhLh!h"hMh jiubah}(h]h]h]h]h]uhjh jiubj)}(hhh]hM)}(hSouth (bottom)h]h/South (bottom)}(hjih jiubah}(h]h]h]h]h]uhhLh!h"hMh jiubah}(h]h]h]h]h]uhjh jiubeh}(h]h]h]h]h]uhjh j.iubj)}(hhh](j)}(hhh]hM)}(h
all, xyf, yxfh]h/
all, xyf, yxf}(hjjh jjubah}(h]h]h]h]h]uhhLh!h"hMh jjubah}(h]h]h]h]h]uhjh j
jubj)}(hhh]hM)}(hAll boundariesh]h/All boundaries}(hj,jh j*jubah}(h]h]h]h]h]uhhLh!h"hMh j'jubah}(h]h]h]h]h]uhjh j
jubeh}(h]h]h]h]h]uhjh j.iubj)}(hhh](j)}(hhh]hM)}(h
+xy, +yx, +fch]h/
+xy, +yx, +fc}(hjLjh jJjubah}(h]h]h]h]h]uhhLh!h"hMh jGjubah}(h]h]h]h]h]uhjh jDjubj)}(hhh]hM)}(hEast (right) + north (top)h]h/East (right) + north (top)}(hjcjh jajubah}(h]h]h]h]h]uhhLh!h"hMh j^jubah}(h]h]h]h]h]uhjh jDjubeh}(h]h]h]h]h]uhjh j.iubj)}(hhh](j)}(hhh]hM)}(h
-xy, -yx, -fch]h/
-xy, -yx, -fc}(hjjh jjubah}(h]h]h]h]h]uhhLh!h"hMh j~jubah}(h]h]h]h]h]uhjh j{jubj)}(hhh]hM)}(hWest (left) + south (bottom)h]h/West (left) + south (bottom)}(hjjh jjubah}(h]h]h]h]h]uhhLh!h"hMh jjubah}(h]h]h]h]h]uhjh j{jubeh}(h]h]h]h]h]uhjh j.iubj)}(hhh](j)}(hhh]hM)}(hxfch]h/xfc}(hjjh jjubah}(h]h]h]h]h]uhhLh!h"hMh jjubah}(h]h]h]h]h]uhjh jjubj)}(hhh]hM)}(hWest (left) + east (right)h]h/West (left) + east (right)}(hjjh jjubah}(h]h]h]h]h]uhhLh!h"hMh jjubah}(h]h]h]h]h]uhjh jjubeh}(h]h]h]h]h]uhjh j.iubj)}(hhh](j)}(hhh]hM)}(hyfch]h/yfc}(hjjh jjubah}(h]h]h]h]h]uhhLh!h"hMh jjubah}(h]h]h]h]h]uhjh jjubj)}(hhh]hM)}(hNorth (top) + south (bottom)h]h/North (top) + south (bottom)}(hjkh jkubah}(h]h]h]h]h]uhhLh!h"hMh jkubah}(h]h]h]h]h]uhjh jjubeh}(h]h]h]h]h]uhjh j.iubj)}(hhh](j)}(hhh]hM)}(h+x+yh]h/+x+y}(hj(kh j&kubah}(h]h]h]h]h]uhhLh!h"hMh j#kubah}(h]h]h]h]h]uhjh j kubj)}(hhh]hM)}(hNortheast (top right)h]h/Northeast (top right)}(hj?kh j=kubah}(h]h]h]h]h]uhhLh!h"hMh j:kubah}(h]h]h]h]h]uhjh j kubeh}(h]h]h]h]h]uhjh j.iubj)}(hhh](j)}(hhh]hM)}(h-x+yh]h/-x+y}(hj_kh j]kubah}(h]h]h]h]h]uhhLh!h"hMh jZkubah}(h]h]h]h]h]uhjh jWkubj)}(hhh]hM)}(hSoutheast (bottom right)h]h/Southeast (bottom right)}(hjvkh jtkubah}(h]h]h]h]h]uhhLh!h"hMh jqkubah}(h]h]h]h]h]uhjh jWkubeh}(h]h]h]h]h]uhjh j.iubj)}(hhh](j)}(hhh]hM)}(h-x-yh]h/-x-y}(hjkh jkubah}(h]h]h]h]h]uhhLh!h"hMh jkubah}(h]h]h]h]h]uhjh jkubj)}(hhh]hM)}(hSouthwest (bottom left)h]h/Southwest (bottom left)}(hjkh jkubah}(h]h]h]h]h]uhhLh!h"hMh jkubah}(h]h]h]h]h]uhjh jkubeh}(h]h]h]h]h]uhjh j.iubj)}(hhh](j)}(hhh]hM)}(h-x+yh]h/-x+y}(hjkh jkubah}(h]h]h]h]h]uhhLh!h"hMh jkubah}(h]h]h]h]h]uhjh jkubj)}(hhh]hM)}(hNorthwest (top left)h]h/Northwest (top left)}(hjkh jkubah}(h]h]h]h]h]uhhLh!h"hMh jkubah}(h]h]h]h]h]uhjh jkubeh}(h]h]h]h]h]uhjh j.iubeh}(h]h]h]h]h]uhjh jhubeh}(h]h]h]h]h]colsKuhjh jhubeh}(h](id195jheh]h]tab9-2-1ah]h]jEcenteruhjh jghhh!h"hNj}jljhsj}jhjhsubh)}(h.. _9-2-3-8:h]h}(h]h]h]h]h]hid98uhh
hMh jghhh!h"ubeh}(h]( boundary-condition-specificationjgeh]h]( boundary condition specification 9-2-3-7-2eh]h]uhh#h jdhhh!h"hMj}j%ljgsj}jgjgsubeh}(h](boundary-conditionsjceh]h](boundary conditions9-2-3-7eh]h]uhh#h jhhh!h"hM#j}j0ljcsj}jcjcsubh$)}(hhh](h))}(hGeneral cross section weightingh]h/General cross section weighting}(hj:lh j8lhhh!NhNubah}(h]h]h]h]h]uhh(h j5lhhh!h"hMubhM)}(hXpNEWT performs cross section weighting by mixture and optionally by
homogenization zone (:ref:`9-2-3-10`). Weighting is always used in
conjunction with an energy collapse. Cross section weighting is
performed over a spatial and energy domain; the resulting average
(weighted) cross sections will preserve all reaction rates in the
collapsed cross section set; that is,h](h/XNEWT performs cross section weighting by mixture and optionally by
homogenization zone (}(hXNEWT performs cross section weighting by mixture and optionally by
homogenization zone (h jFlhhh!NhNubj)}(h:ref:`9-2-3-10`h]j)}(hjQlh]h/9-2-3-10}(hhh jSlubah}(h]h](jEstdstd-refeh]h]h]uhjh jOlubah}(h]h]h]h]h]refdochj refdomainj]lreftyperefrefexplicitrefwarnjW9-2-3-10uhjh!h"hMh jFlubh/X ). Weighting is always used in
conjunction with an energy collapse. Cross section weighting is
performed over a spatial and energy domain; the resulting average
(weighted) cross sections will preserve all reaction rates in the
collapsed cross section set; that is,}(hX ). Weighting is always used in
conjunction with an energy collapse. Cross section weighting is
performed over a spatial and energy domain; the resulting average
(weighted) cross sections will preserve all reaction rates in the
collapsed cross section set; that is,h jFlhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j5lhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-28uhh
h j5lhhh!h"hNubj))}(h\sigma_{G}^{i}=\frac{\int_{r} N^{i}(r) d r \int_{G} \sigma^{i}(E, r) W(E, r) d E}{\int_{r} N^{i}(r) d r \int_{G} W(E, r) d E} ,h]h/\sigma_{G}^{i}=\frac{\int_{r} N^{i}(r) d r \int_{G} \sigma^{i}(E, r) W(E, r) d E}{\int_{r} N^{i}(r) d r \int_{G} W(E, r) d E} ,}(hhh jlubah}(h]jlah]h]h]h]docnamehjnumberKlabeleq9-2-28nowrapj=j>uhj(h!h"hMh j5lhhj}j}jljzlsubhM)}(hwhereh]h/where}(hjlh jlhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM
h j5lhhubjP)}(hhh](hM)}(hg:math:`\sigma_{G}^{i}` ≡ average (weighted) cross section in energy group \ *G* for
nuclide \ *I*,h](jY)}(h:math:`\sigma_{G}^{i}`h]h/\sigma_{G}^{i}}(hhh jlubah}(h]h]h]h]h]uhjXh jlubh/: ≡ average (weighted) cross section in energy group }(h: ≡ average (weighted) cross section in energy group \ h jlubj)}(h*G*h]h/G}(hhh jlubah}(h]h]h]h]h]uhjh jlubh/ for
nuclide }(h for
nuclide \ h jlubj)}(h*I*h]h/I}(hhh jlubah}(h]h]h]h]h]uhjh jlubh/,}(hjzh jlubeh}(h]h]h]h]h]uhhLh!h"hM
h jlubhM)}(hA:math:`N^{i}(r)` ≡ number density of nuclide *i* in region *r*,h](jY)}(h:math:`N^{i}(r)`h]h/N^{i}(r)}(hhh jlubah}(h]h]h]h]h]uhjXh jlubh/ ≡ number density of nuclide }(h ≡ number density of nuclide h jlubj)}(h*i*h]h/i}(hhh jmubah}(h]h]h]h]h]uhjh jlubh/ in region }(h in region h jlubj)}(h*r*h]h/r}(hhh jmubah}(h]h]h]h]h]uhjh jlubh/,}(hjzh jlubeh}(h]h]h]h]h]uhhLh!h"hM
h jlubhM)}(h=:math:`W(E, r)` ≡ the weighting function within region *r,*h](jY)}(h:math:`W(E, r)`h]h/W(E, r)}(hhh j2mubah}(h]h]h]h]h]uhjXh j.mubh/* ≡ the weighting function within region }(h* ≡ the weighting function within region h j.mubj)}(h*r,*h]h/r,}(hhh jEmubah}(h]h]h]h]h]uhjh j.mubeh}(h]h]h]h]h]uhhLh!h"hM
h jlubhM)}(hk:math:`\sigma^{i}(E, r)` ≡ the cross section from the input library for nuclide \ *i* in
region \ *r*.h](jY)}(h:math:`\sigma^{i}(E, r)`h]h/\sigma^{i}(E, r)}(hhh j]mubah}(h]h]h]h]h]uhjXh jYmubh/> ≡ the cross section from the input library for nuclide }(h> ≡ the cross section from the input library for nuclide \ h jYmubj)}(h*i*h]h/i}(hhh jpmubah}(h]h]h]h]h]uhjh jYmubh/ in
region }(h in
region \ h jYmubj)}(h*r*h]h/r}(hhh jmubah}(h]h]h]h]h]uhjh jYmubh/.}(hhh jYmubeh}(h]h]h]h]h]uhhLh!h"hM
h jlubeh}(h]h]h]h]h]uhjOh j5lhhh!h"hNubhM)}(hXWithin NEWT, each collapsing region is the spatial region or regions in
which a given mixture is placed. Hence, for most of the cross section
types, an average cross section for the mixture associated with the
spatial domain *r* (which may include one or more defined regions
occupied by that mixture) is calculated by weighting the original
problem-specific cross section data for that mixture using as a
weighting function the neutron spectrum calculated within spatial domain
*r*.h](h/Within NEWT, each collapsing region is the spatial region or regions in
which a given mixture is placed. Hence, for most of the cross section
types, an average cross section for the mixture associated with the
spatial domain }(hWithin NEWT, each collapsing region is the spatial region or regions in
which a given mixture is placed. Hence, for most of the cross section
types, an average cross section for the mixture associated with the
spatial domain h jmhhh!NhNubj)}(h*r*h]h/r}(hhh jmubah}(h]h]h]h]h]uhjh jmubh/ (which may include one or more defined regions
occupied by that mixture) is calculated by weighting the original
problem-specific cross section data for that mixture using as a
weighting function the neutron spectrum calculated within spatial domain
}(h (which may include one or more defined regions
occupied by that mixture) is calculated by weighting the original
problem-specific cross section data for that mixture using as a
weighting function the neutron spectrum calculated within spatial domain
h jmhhh!NhNubj)}(h*r*h]h/r}(hhh jmubah}(h]h]h]h]h]uhjh jmubh/.}(hhh jmhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM
h j5lhhubhM)}(hzIn practice, the integration of :eq:`eq9-2-28` is performed as a simple
summation over all cells *j* within region \ *r*:h](h/ In practice, the integration of }(h In practice, the integration of h jmhhh!NhNubj)}(h:eq:`eq9-2-28`h]jM)}(hjmh]h/eq9-2-28}(hhh jmubah}(h]h](jEeqeh]h]h]uhjLh jmubah}(h]h]h]h]h]refdochj refdomainjXreftypejmrefexplicitrefwarnjWeq9-2-28uhjh!h"hM
h jmubh/3 is performed as a simple
summation over all cells }(h3 is performed as a simple
summation over all cells h jmhhh!NhNubj)}(h*j*h]h/j}(hhh jnubah}(h]h]h]h]h]uhjh jmubh/ within region }(h within region \ h jmhhh!NhNubj)}(h*r*h]h/r}(hhh jnubah}(h]h]h]h]h]uhjh jmubh/:}(h:h jmhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM
h j5lhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-29uhh
h j5lhhh!h"hNubj))}(h\sigma_{i, G}=\frac{N_{r}^{i} \sum_{j \in r} \sum_{g \in G} \sigma_{g, j}^{i} W_{g, j}}{N_{r}^{i} \sum_{j \in r} \sum_{g \in G} W_{g, j}} .h]h/\sigma_{i, G}=\frac{N_{r}^{i} \sum_{j \in r} \sum_{g \in G} \sigma_{g, j}^{i} W_{g, j}}{N_{r}^{i} \sum_{j \in r} \sum_{g \in G} W_{g, j}} .}(hhh j7nubah}(h]j6nah]h]h]h]docnamehjnumberKlabeleq9-2-29nowrapj=j>uhj(h!h"hM
h j5lhhj}j}j6nj-nsubhM)}(hBecause any region *r* is defined as the sum of all spatial regions
containing a given mixture, is constant everywhere within *r*.h](h/Because any region }(hBecause any region h jLnhhh!NhNubj)}(h*r*h]h/r}(hhh jUnubah}(h]h]h]h]h]uhjh jLnubh/h is defined as the sum of all spatial regions
containing a given mixture, is constant everywhere within }(hh is defined as the sum of all spatial regions
containing a given mixture, is constant everywhere within h jLnhhh!NhNubj)}(h*r*h]h/r}(hhh jhnubah}(h]h]h]h]h]uhjh jLnubh/.}(hhh jLnhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM!
h j5lhhubhM)}(hXAll multigroup cross sections and related data present on the AMPX
library are weighted using appropriate weighting functions. For most
basic cross sections, the multigroup flux obtained from the transport
solution is the appropriate weighting function and :math:`W_{g, r}` in :eq:`eq9-2-29`
becomes :math:`\phi_{g, r}`. However, special cross sections and data need special
treatment, as described in the following sections.h](h/XAll multigroup cross sections and related data present on the AMPX
library are weighted using appropriate weighting functions. For most
basic cross sections, the multigroup flux obtained from the transport
solution is the appropriate weighting function and }(hXAll multigroup cross sections and related data present on the AMPX
library are weighted using appropriate weighting functions. For most
basic cross sections, the multigroup flux obtained from the transport
solution is the appropriate weighting function and h jnhhh!NhNubjY)}(h:math:`W_{g, r}`h]h/W_{g, r}}(hhh jnubah}(h]h]h]h]h]uhjXh jnubh/ in }(h in h jnhhh!NhNubj)}(h:eq:`eq9-2-29`h]jM)}(hjnh]h/eq9-2-29}(hhh jnubah}(h]h](jEeqeh]h]h]uhjLh jnubah}(h]h]h]h]h]refdochj refdomainjXreftypejnrefexplicitrefwarnjWeq9-2-29uhjh!h"hM$
h jnubh/
becomes }(h
becomes h jnhhh!NhNubjY)}(h:math:`\phi_{g, r}`h]h/\phi_{g, r}}(hhh jnubah}(h]h]h]h]h]uhjXh jnubh/k. However, special cross sections and data need special
treatment, as described in the following sections.}(hk. However, special cross sections and data need special
treatment, as described in the following sections.h jnhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM$
h j5lhhubh)}(h.. _9-2-3-8-1:h]h}(h]h]h]h]h]hid99uhh
hM+
h j5lhhh!h"ubh$)}(hhh](h))}(h2Scattering cross section transfer matrix weightingh]h/2Scattering cross section transfer matrix weighting}(hjnh jnhhh!NhNubah}(h]h]h]h]h]uhh(h jnhhh!h"hM.
ubhM)}(h\In weighting scattering cross sections, the form of the weighting is
slightly more complex:h]h/\In weighting scattering cross sections, the form of the weighting is
slightly more complex:}(hjnh jnhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM0
h jnhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-30uhh
h jnhhh!h"hNubj))}(h\sigma_{s, G \rightarrow G^{\prime}}^{i}=\frac{\int_{r} N^{i}(r) d r \int_{G} W(E, r) d E \int_{G^{\prime}} \sigma^{i}\left(E \rightarrow E^{\prime}, r\right) d E^{\prime}}{\int_{r} N^{i}(r) d r \int_{G} W(E, r) d E} ,h]h/\sigma_{s, G \rightarrow G^{\prime}}^{i}=\frac{\int_{r} N^{i}(r) d r \int_{G} W(E, r) d E \int_{G^{\prime}} \sigma^{i}\left(E \rightarrow E^{\prime}, r\right) d E^{\prime}}{\int_{r} N^{i}(r) d r \int_{G} W(E, r) d E} ,}(hhh joubah}(h]joah]h]h]h]docnamehjnumberKlabeleq9-2-30nowrapj=j>uhj(h!h"hM3
h jnhhj}j}jojosubhM)}(hor, in multigroup format,h]h/or, in multigroup format,}(hj#oh j!ohhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM8
h jnhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-31uhh
h jnhhh!h"hNubj))}(h\sigma_{s, G \rightarrow G^{\prime}}^{i}=\frac{N_{r}^{i} \sum_{j \in r} \sum_{g \in G} W_{g, r} \sum_{g^{\prime} \in G^{\prime}} \sigma^{i}\left(g \rightarrow g^{\prime}\right)}{N_{r}^{i} \sum_{j \in r} \sum_{g \in G} W_{g, r}} .h]h/\sigma_{s, G \rightarrow G^{\prime}}^{i}=\frac{N_{r}^{i} \sum_{j \in r} \sum_{g \in G} W_{g, r} \sum_{g^{\prime} \in G^{\prime}} \sigma^{i}\left(g \rightarrow g^{\prime}\right)}{N_{r}^{i} \sum_{j \in r} \sum_{g \in G} W_{g, r}} .}(hhh j9oubah}(h]j8oah]h]h]h]docnamehjnumberKlabeleq9-2-31nowrapj=j>uhj(h!h"hM:
h jnhhj}j}j8oj/osubhM)}(hsIn general, the scalar flux, *ϕ*\ :sub:`g,r` is the appropriate weighting
function for scattering cross sections:h](h/In general, the scalar flux, }(hIn general, the scalar flux, h jNohhh!NhNubj)}(h*ϕ*h]h/ϕ}(hhh jWoubah}(h]h]h]h]h]uhjh jNoubh/ }(h\ h jNohhh!NhNubj)}(h
:sub:`g,r`h]h/g,r}(hhh jjoubah}(h]h]h]h]h]uhjh jNoubh/F is the appropriate weighting
function for scattering cross sections:}(hF is the appropriate weighting
function for scattering cross sections:h jNohhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM?
h jnhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-32uhh
h jnhhh!h"hNubj))}(h\sigma_{G}^{i}=\frac{N_{r}^{i} \sum_{j \in r} \sum_{g \in G} \sigma_{g, r}^{i} \phi_{g, r}}{N_{r}^{i} \sum_{j \in r} \sum_{g \in G} \phi_{g, r}} .h]h/\sigma_{G}^{i}=\frac{N_{r}^{i} \sum_{j \in r} \sum_{g \in G} \sigma_{g, r}^{i} \phi_{g, r}}{N_{r}^{i} \sum_{j \in r} \sum_{g \in G} \phi_{g, r}} .}(hhh joubah}(h]joah]h]h]h]docnamehjnumberK labeleq9-2-32nowrapj=j>uhj(h!h"hMB
h jnhhj}j}jojosubhM)}(hXThis is an approximation for the higher order moments (*l* > 0) of the
scattering cross sections, which should be more properly weighted using
the *l*\ th moment of the flux instead of the 0th moment (scalar) flux
as used in Eq. :eq:`eq9-2-32`. However, because flux moments are generally
both positive and negative, NEWT performs higher-order-moment scattering
cross section weighting using the positive scalar flux.h](h/7This is an approximation for the higher order moments (}(h7This is an approximation for the higher order moments (h johhh!NhNubj)}(h*l*h]h/l}(hhh joubah}(h]h]h]h]h]uhjh joubh/\ > 0) of the
scattering cross sections, which should be more properly weighted using
the }(h\ > 0) of the
scattering cross sections, which should be more properly weighted using
the h johhh!NhNubj)}(h*l*h]h/l}(hhh joubah}(h]h]h]h]h]uhjh joubh/P th moment of the flux instead of the 0th moment (scalar) flux
as used in Eq. }(hP\ th moment of the flux instead of the 0th moment (scalar) flux
as used in Eq. h johhh!NhNubj)}(h:eq:`eq9-2-32`h]jM)}(hjoh]h/eq9-2-32}(hhh joubah}(h]h](jEeqeh]h]h]uhjLh joubah}(h]h]h]h]h]refdochj refdomainjXreftypejorefexplicitrefwarnjWeq9-2-32uhjh!h"hMG
h joubh/. However, because flux moments are generally
both positive and negative, NEWT performs higher-order-moment scattering
cross section weighting using the positive scalar flux.}(h. However, because flux moments are generally
both positive and negative, NEWT performs higher-order-moment scattering
cross section weighting using the positive scalar flux.h johhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMG
h jnhhubh)}(h.. _9-2-3-8-2:h]h}(h]h]h]h]h]hid100uhh
hMN
h jnhhh!h"ubeh}(h](2scattering-cross-section-transfer-matrix-weightingjneh]h](2scattering cross section transfer matrix weighting 9-2-3-8-1eh]h]uhh#h j5lhhh!h"hM.
j}jpjnsj}jnjnsubh$)}(hhh](h))}(h9Weighting of the collapsed fission spectrum, :math:`\chi`h](h/-Weighting of the collapsed fission spectrum, }(h-Weighting of the collapsed fission spectrum, h jphhh!NhNubjY)}(h:math:`\chi`h]h/\chi}(hhh jpubah}(h]h]h]h]h]uhjXh jpubeh}(h]h]h]h]h]uhh(h jphhh!h"hMQ
ubhM)}(hXWeighting is not required for collapsing a fission spectrum vector; the
format for a collapsed fission spectrum (χ\ :sub:`G`) is a very
straightforward summation of the fission spectra in energy groups \ *g*
spanning the energy domain of the collapsed energy group \ *G*:h](h/uWeighting is not required for collapsing a fission spectrum vector; the
format for a collapsed fission spectrum (χ }(huWeighting is not required for collapsing a fission spectrum vector; the
format for a collapsed fission spectrum (χ\ h j0phhh!NhNubj)}(h:sub:`G`h]h/G}(hhh j9pubah}(h]h]h]h]h]uhjh j0pubh/Q) is a very
straightforward summation of the fission spectra in energy groups }(hQ) is a very
straightforward summation of the fission spectra in energy groups \ h j0phhh!NhNubj)}(h*g*h]h/g}(hhh jLpubah}(h]h]h]h]h]uhjh j0pubh/=
spanning the energy domain of the collapsed energy group }(h=
spanning the energy domain of the collapsed energy group \ h j0phhh!NhNubj)}(h*G*h]h/G}(hhh j_pubah}(h]h]h]h]h]uhjh j0pubh/:}(hj&nh j0phhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMS
h jphhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-33uhh
h jphhh!h"hNubj))}(h"\chi_{G}=\sum_{g \in G} \chi_{g} .h]h/"\chi_{G}=\sum_{g \in G} \chi_{g} .}(hhh jpubah}(h]jpah]h]h]h]docnamehjnumberK!labeleq9-2-33nowrapj=j>uhj(h!h"hMX
h jphhj}j}jpjwpsubh)}(h.. _9-2-3-8-3:h]h}(h]h]h]h]h]hid101uhh
hM]
h jphhh!h"ubeh}(h](/weighting-of-the-collapsed-fission-spectrum-chijpeh]h](1weighting of the collapsed fission spectrum, \chi 9-2-3-8-2eh]h]uhh#h j5lhhh!h"hMQ
j}jpjosj}jpjosubh$)}(hhh](h))}(hGWeighting of the number of neutrons per fission, :math:`\boldsymbol{V}`h](h/1Weighting of the number of neutrons per fission, }(h1Weighting of the number of neutrons per fission, h jphhh!NhNubjY)}(h:math:`\boldsymbol{V}`h]h/\boldsymbol{V}}(hhh jpubah}(h]h]h]h]h]uhjXh jpubeh}(h]h]h]h]h]uhh(h jphhh!h"hM`
ubhM)}(hnAccurate weighting of :math:`v` in an energy and space domain requires weighting
by the fission rate; that is,h](h/Accurate weighting of }(hAccurate weighting of h jphhh!NhNubjY)}(h :math:`v`h]h/v}(hhh jpubah}(h]h]h]h]h]uhjXh jpubh/O in an energy and space domain requires weighting
by the fission rate; that is,}(hO in an energy and space domain requires weighting
by the fission rate; that is,h jphhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMb
h jphhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-34uhh
h jphhh!h"hNubj))}(h8W(E, r)=\sigma_{\text {fission }}^{i}(E, r) \phi(E, r) .h]h/8W(E, r)=\sigma_{\text {fission }}^{i}(E, r) \phi(E, r) .}(hhh jpubah}(h]jpah]h]h]h]docnamehjnumberK"labeleq9-2-34nowrapj=j>uhj(h!h"hMe
h jphhj}j}jpjpsubhM)}(h6Hence, for :math:`v`, Eq. :eq:`eq9-2-32` has the formh](h/Hence, for }(hHence, for h j
qhhh!NhNubjY)}(h :math:`v`h]h/v}(hhh jqubah}(h]h]h]h]h]uhjXh j
qubh/, Eq. }(h, Eq. h j
qhhh!NhNubj)}(h:eq:`eq9-2-32`h]jM)}(hj+qh]h/eq9-2-32}(hhh j-qubah}(h]h](jEeqeh]h]h]uhjLh j)qubah}(h]h]h]h]h]refdochj refdomainjXreftypej7qrefexplicitrefwarnjWeq9-2-32uhjh!h"hMj
h j
qubh/
has the form}(h
has the formh j
qhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMj
h jphhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-35uhh
h jphhh!h"hNubj))}(hv_{G}^{i}=\frac{N_{r}^{i} \sum_{j \in r} \sum_{g \in G} v_{g}^{i} \sigma_{f i s s i o n, g, r}^{i} \phi_{g, r}}{N_{r}^{i} \sum_{j \in r} \sum_{g \in G} \sigma_{f i s s i o n, g, r}^{i} \phi_{g, r}} .h]h/v_{G}^{i}=\frac{N_{r}^{i} \sum_{j \in r} \sum_{g \in G} v_{g}^{i} \sigma_{f i s s i o n, g, r}^{i} \phi_{g, r}}{N_{r}^{i} \sum_{j \in r} \sum_{g \in G} \sigma_{f i s s i o n, g, r}^{i} \phi_{g, r}} .}(hhh j\qubah}(h]j[qah]h]h]h]docnamehjnumberK#labeleq9-2-35nowrapj=j>uhj(h!h"hMl
h jphhj}j}j[qjRqsubh)}(h.. _9-2-3-8-4:h]h}(h]h]h]h]h]hid102uhh
hMq
h jphhh!h"ubeh}(h](uhj(h!h"hM
h jqhhj}j}jqjqsubhM)}(hThe (n,2n) reaction rates reported in NEWT output are those computed for
the effective cross section. The effective (n,2n) cross section is not
saved to the weighted library.h]h/The (n,2n) reaction rates reported in NEWT output are those computed for
the effective cross section. The effective (n,2n) cross section is not
saved to the weighted library.}(hjqh jqhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM
h jqhhubh)}(h.. _9-2-3-8-5:h]h}(h]h]h]h]h]hid103uhh
hM
h jqhhh!h"ubeh}(h](.weighting-of-n-2n-n-3n-and-n-4n-cross-sectionsj{qeh]h](6weighting of (n,2n), (n,3n), and (n,4n) cross sections 9-2-3-8-4eh]h]uhh#h j5lhhh!h"hMt
j}jrjqqsj}j{qjqqsubh$)}(hhh](h))}(h5Calculation and weighting of transport cross sectionsh]h/5Calculation and weighting of transport cross sections}(hj rh jrhhh!NhNubah}(h]h]h]h]h]uhh(h jrhhh!h"hM
ubhM)}(hXaTransport cross sections are processed in a different manner from other
cross sections. The transport cross section does not represent a purely
measurable quantity. Introduced within the P\ :sub:`1` (diffusion)
approximation to the neutron transport equation, it attempts to preserve
a flux gradient in addition to reaction rate information. Hence, the
magnitude of a microscopic transport cross section is affected by both
the physics properties of the nuclide in question and the geometrical
attributes of the spatial domain where the nuclide resides and the other
nuclides present in the same vicinity.h](h/Transport cross sections are processed in a different manner from other
cross sections. The transport cross section does not represent a purely
measurable quantity. Introduced within the P }(hTransport cross sections are processed in a different manner from other
cross sections. The transport cross section does not represent a purely
measurable quantity. Introduced within the P\ h j,rhhh!NhNubj)}(h:sub:`1`h]h/1}(hhh j5rubah}(h]h]h]h]h]uhjh j,rubh/X (diffusion)
approximation to the neutron transport equation, it attempts to preserve
a flux gradient in addition to reaction rate information. Hence, the
magnitude of a microscopic transport cross section is affected by both
the physics properties of the nuclide in question and the geometrical
attributes of the spatial domain where the nuclide resides and the other
nuclides present in the same vicinity.}(hX (diffusion)
approximation to the neutron transport equation, it attempts to preserve
a flux gradient in addition to reaction rate information. Hence, the
magnitude of a microscopic transport cross section is affected by both
the physics properties of the nuclide in question and the geometrical
attributes of the spatial domain where the nuclide resides and the other
nuclides present in the same vicinity.h j,rhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM
h jrhhubhM)}(hXbConsistent with XSDRNPM, NEWT provides two options to generate a
microscopic transport cross section—based on the “consistent” and
“inconsistent” methods for solving the P\ :sub:`l` transport equations.
These approximations are referred to as the “outscatter” and “inscatter”
approximations because of the nature of the equations used.h](h/Consistent with XSDRNPM, NEWT provides two options to generate a
microscopic transport cross section—based on the “consistent” and
“inconsistent” methods for solving the P }(hConsistent with XSDRNPM, NEWT provides two options to generate a
microscopic transport cross section—based on the “consistent” and
“inconsistent” methods for solving the P\ h jNrhhh!NhNubj)}(h:sub:`l`h]h/l}(hhh jWrubah}(h]h]h]h]h]uhjh jNrubh/ transport equations.
These approximations are referred to as the “outscatter” and “inscatter”
approximations because of the nature of the equations used.}(h transport equations.
These approximations are referred to as the “outscatter” and “inscatter”
approximations because of the nature of the equations used.h jNrhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM
h jrhhubh)}(h.. _9-2-3-8-5-1:h]h}(h]h]h]h]h]hid104uhh
hM
h jrhhh!h"ubh$)}(hhh](h))}(h.Outscatter approximation (inconsistent method)h]h/.Outscatter approximation (inconsistent method)}(hjrh j~rhhh!NhNubah}(h]h]h]h]h]uhh(h j{rhhh!h"hM
ubhM)}(hsIn the outscatter approximation, the following assumption is made for
the transport cross section in group \ *g*:h](h/oIn the outscatter approximation, the following assumption is made for
the transport cross section in group }(hoIn the outscatter approximation, the following assumption is made for
the transport cross section in group \ h jrhhh!NhNubj)}(h*g*h]h/g}(hhh jrubah}(h]h]h]h]h]uhjh jrubh/:}(hj&nh jrhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM
h j{rhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-37uhh
h j{rhhh!h"hNubj))}(h>\sigma_{t r}^{g}=\sigma_{t}^{g}-\bar{\mu}^{g} \sigma_{s}^{g} ,h]h/>\sigma_{t r}^{g}=\sigma_{t}^{g}-\bar{\mu}^{g} \sigma_{s}^{g} ,}(hhh jrubah}(h]jrah]h]h]h]docnamehjnumberK%labeleq9-2-37nowrapj=j>uhj(h!h"hM
h j{rhhj}j}jrjrsubhM)}(htwhere σ\ :sub:`t`\ :sup:`g` and σ\ :sub:`s`\ :sup:`g` are the total and
scattering cross section in group \ *g*,h](h/
where σ }(h
where σ\ h jrhhh!NhNubj)}(h:sub:`t`h]h/t}(hhh jrubah}(h]h]h]h]h]uhjh jrubh/ }(h\ h jrhhh!NhNubjY)}(h:sup:`g`h]h/g}(hhh jrubah}(h]h]h]h]h]uhjXh jrubh/ and σ }(h and σ\ h jrhhh!NhNubj)}(h:sub:`s`h]h/s}(hhh jrubah}(h]h]h]h]h]uhjh jrubh/ }(hjrh jrubjY)}(h:sup:`g`h]h/g}(hhh j
subah}(h]h]h]h]h]uhjXh jrubh/9 are the total and
scattering cross section in group }(h9 are the total and
scattering cross section in group \ h jrhhh!NhNubj)}(h*g*h]h/g}(hhh j subah}(h]h]h]h]h]uhjh jrubh/,}(hjzh jrhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM
h j{rhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-38uhh
h j{rhhh!h"hNubj))}(h;\bar{\mu}^{g}=\frac{\sigma_{s, 1}^{g}}{3 \sigma_{s, 0}^{g}}h]h/;\bar{\mu}^{g}=\frac{\sigma_{s, 1}^{g}}{3 \sigma_{s, 0}^{g}}}(hhh jBsubah}(h]jAsah]h]h]h]docnamehjnumberK&labeleq9-2-38nowrapj=j>uhj(h!h"hM
h j{rhhj}j}jAsj8ssubhM)}(handh]h/and}(hjYsh jWshhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM
h j{rhhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-39uhh
h j{rhhh!h"hNubj))}(hX\sigma_{s, N}^{g}=\sum_{g^{\prime}} \sigma_{s, N}\left(g \rightarrow g^{\prime}\right) .h]h/X\sigma_{s, N}^{g}=\sum_{g^{\prime}} \sigma_{s, N}\left(g \rightarrow g^{\prime}\right) .}(hhh josubah}(h]jnsah]h]h]h]docnamehjnumberK'labeleq9-2-39nowrapj=j>uhj(h!h"hM
h j{rhhj}j}jnsjessubhM)}(hNote that the :math:`\sigma_{s, N}\left(g \rightarrow g^{\prime}\right)` terms are the P\ :sub:`N` coefficients of the scattering
matrix, hence the origin of the term “outscatter.”h](h/Note that the }(hNote that the h jshhh!NhNubjY)}(h::math:`\sigma_{s, N}\left(g \rightarrow g^{\prime}\right)`h]h/2\sigma_{s, N}\left(g \rightarrow g^{\prime}\right)}(hhh jsubah}(h]h]h]h]h]uhjXh jsubh/ terms are the P }(h terms are the P\ h jshhh!NhNubj)}(h:sub:`N`h]h/N}(hhh jsubah}(h]h]h]h]h]uhjh jsubh/V coefficients of the scattering
matrix, hence the origin of the term “outscatter.”}(hV coefficients of the scattering
matrix, hence the origin of the term “outscatter.”h jshhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM
h j{rhhubh)}(h.. _9-2-3-8-5-2:h]h}(h]h]h]h]h]hid105uhh
hM
h j{rhhh!h"ubeh}(h](,outscatter-approximation-inconsistent-methodjzreh]h](.outscatter approximation (inconsistent method)9-2-3-8-5-1eh]h]uhh#h jrhhh!h"hM
j}jsjprsj}jzrjprsubh$)}(hhh](h))}(h+Inscatter approximation (consistent method)h]h/+Inscatter approximation (consistent method)}(hjsh jshhh!NhNubah}(h]h]h]h]h]uhh(h jshhh!h"hM
ubhM)}(hwIn the “consistent” P\ :sub:`1` approximation of the transport equation,
the transport cross section is defined ash](h/In the “consistent” P }(hIn the “consistent” P\ h jshhh!NhNubj)}(h:sub:`1`h]h/1}(hhh jsubah}(h]h]h]h]h]uhjh jsubh/T approximation of the transport equation,
the transport cross section is defined as}(hT approximation of the transport equation,
the transport cross section is defined ash jshhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM
h jshhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-40uhh
h jshhh!h"hNubj))}(h\sigma_{t r}(E)=\sigma_{t}(E)-\frac{1}{3 J(E)} \int_{0}^{\infty} \sigma_{s, 1}\left(E^{\prime} \rightarrow E\right) J\left(E^{\prime}\right) d E^{\prime}h]h/\sigma_{t r}(E)=\sigma_{t}(E)-\frac{1}{3 J(E)} \int_{0}^{\infty} \sigma_{s, 1}\left(E^{\prime} \rightarrow E\right) J\left(E^{\prime}\right) d E^{\prime}}(hhh jtubah}(h]jtah]h]h]h]docnamehjnumberK(labeleq9-2-40nowrapj=j>uhj(h!h"hM
h jshhj}j}jtjtsubhM)}(hwhere *J* is the neutron current and :math:`\sigma_{s, 1}` is the first moment (P\ :sub:`1`
coefficient) of the scattering transfer matrix.h](h/where }(hwhere h j!thhh!NhNubj)}(h*J*h]h/J}(hhh j*tubah}(h]h]h]h]h]uhjh j!tubh/ is the neutron current and }(h is the neutron current and h j!thhh!NhNubjY)}(h:math:`\sigma_{s, 1}`h]h/
\sigma_{s, 1}}(hhh j=tubah}(h]h]h]h]h]uhjXh j!tubh/ is the first moment (P }(h is the first moment (P\ h j!thhh!NhNubj)}(h:sub:`1`h]h/1}(hhh jPtubah}(h]h]h]h]h]uhjh j!tubh/0
coefficient) of the scattering transfer matrix.}(h0
coefficient) of the scattering transfer matrix.h j!thhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM
h jshhubhM)}(hIf one multiplies Eq. :eq:`eq9-2-40` by J(E), integrates over group \ *g*, and
converts to a group-averaged form by dividing by :math:`\int_{g} J(E) d E`, the following
expression is derived:h](h/If one multiplies Eq. }(hIf one multiplies Eq. h jithhh!NhNubj)}(h:eq:`eq9-2-40`h]jM)}(hjtth]h/eq9-2-40}(hhh jvtubah}(h]h](jEeqeh]h]h]uhjLh jrtubah}(h]h]h]h]h]refdochj refdomainjXreftypejtrefexplicitrefwarnjWeq9-2-40uhjh!h"hM
h jitubh/# by J(E), integrates over group }(h# by J(E), integrates over group \ h jithhh!NhNubj)}(h*g*h]h/g}(hhh jtubah}(h]h]h]h]h]uhjh jitubh/7, and
converts to a group-averaged form by dividing by }(h7, and
converts to a group-averaged form by dividing by h jithhh!NhNubjY)}(h:math:`\int_{g} J(E) d E`/h]h/\int_{g} J(E) d E}(hhh jtubah}(h]h]h]h]h]uhjXh jitubh/&, the following
expression is derived:}(h&, the following
expression is derived:h jithhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM
h jshhubh)}(hhh]h}(h]h]h]h]h]hequation-eq9-2-41uhh
h jshhh!h"hNubj))}(h\sigma_{t r}^{g}=\sigma_{t}^{g}-\frac{1}{3 J_{g}} \sum_{g^{\prime}} \sigma_{s, 1}\left(g^{\prime} \rightarrow g\right) J_{g^{\prime}} .h]h/\sigma_{t r}^{g}=\sigma_{t}^{g}-\frac{1}{3 J_{g}} \sum_{g^{\prime}} \sigma_{s, 1}\left(g^{\prime} \rightarrow g\right) J_{g^{\prime}} .}(hhh jtubah}(h]jtah]h]h]h]docnamehjnumberK)labeleq9-2-41nowrapj=j>uhj(h!h"hM
h jshhj}j}jtjtsubhM)}(hThis is the “inscatter” approximation. It is consistent because the
transport values are explicitly derived from the P\ :sub:`0` and
P\ :sub:`1` equations.h](h/|This is the “inscatter” approximation. It is consistent because the
transport values are explicitly derived from the P }(h|This is the “inscatter” approximation. It is consistent because the
transport values are explicitly derived from the P\ h jthhh!NhNubj)}(h:sub:`0`h]h/0}(hhh jtubah}(h]h]h]h]h]uhjh jtubh/ and
P }(h and
P\ h jthhh!NhNubj)}(h:sub:`1`h]h/1}(hhh jtubah}(h]h]h]h]h]uhjh jtubh/ equations.}(h equations.h jthhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM
h jshhubeh}(h]()inscatter-approximation-consistent-methodjseh]h](+inscatter approximation (consistent method)9-2-3-8-5-2eh]h]uhh#h jrhhh!h"hM
j}jujssj}jsjssubh$)}(hhh](h))}(h.Weighting function for transport cross sectionh]h/.Weighting function for transport cross section}(hj%uh j#uhhh!NhNubah}(h]h]h]h]h]uhh(h j uhhh!h"hM
ubhM)}(hXInternal investigations have shown that transport cross sections
computed using the “outscatter” approximation are more robust in
subsequent nodal core calculations as compared with transport cross
sections computed using the “inscatter approximation.” NEWT computes
transport cross sections using the outscatter approximation and
collapses the cross section with the scalar flux.h]h/XInternal investigations have shown that transport cross sections
computed using the “outscatter” approximation are more robust in
subsequent nodal core calculations as compared with transport cross
sections computed using the “inscatter approximation.” NEWT computes
transport cross sections using the outscatter approximation and
collapses the cross section with the scalar flux.}(hj3uh j1uhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM
h j uhhubh)}(h.. _9-2-3-9:h]h}(h]h]h]h]h]hid106uhh
hM
h j uhhh!h"ubeh}(h].weighting-function-for-transport-cross-sectionah]h].weighting function for transport cross sectionah]h]uhh#h jrhhh!h"hM
ubeh}(h](5calculation-and-weighting-of-transport-cross-sectionsjreh]h](5calculation and weighting of transport cross sections 9-2-3-8-5eh]h]uhh#h j5lhhh!h"hM
j}jXujrsj}jrjrsubeh}(h](general-cross-section-weightingjleh]h](general cross section weighting9-2-3-8eh]h]uhh#h jhhh!h"hMj}jcujlsj}jljlsubh$)}(hhh](h))}(hArray definitionh]h/Array definition}(hjmuh jkuhhh!NhNubah}(h]h]h]h]h]uhh(h jhuhhh!h"hM
ubhM)}(hAny arrays specified in unit definitions within the *read geom* block
are defined in terms of form and content in the *read array* data block.
The block has the form shown below:h](h/4Any arrays specified in unit definitions within the }(h4Any arrays specified in unit definitions within the h jyuhhh!NhNubj)}(h*read geom*h]h/ read geom}(hhh juubah}(h]h]h]h]h]uhjh jyuubh/7 block
are defined in terms of form and content in the }(h7 block
are defined in terms of form and content in the h jyuhhh!NhNubj)}(h*read array*h]h/
read array}(hhh juubah}(h]h]h]h]h]uhjh jyuubh/0 data block.
The block has the form shown below:}(h0 data block.
The block has the form shown below:h jyuhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM
h jhuhhubjH)}(hsread array
ara=arrayid nux=nx nuy=ny typ=aratype [pinpow=yes/no]
fill i1 i2 i3 i4 … iN end fill
…
end arrayh]h/sread array
ara=arrayid nux=nx nuy=ny typ=aratype [pinpow=yes/no]
fill i1 i2 i3 i4 … iN end fill
…
end array}(hhh juubah}(h]h]h]h]h]j=j>uhjGh!h"hM
h jhuhhubhM)}(hXYwhere *arrayid* is a unique integer identifier for the array, *nx* is
the number of array elements moving left to right (i.e., columns), and
*ny* is the number of array elements moving from bottom to top
(i.e., rows). The type of array is indicated by *aratype* (e.g., square,
hexagonal). The optional parameter *pinpow* may be specified as either
*yes* or *no* (default is no) and is used to enable/disable pin power
edits for units within the array. The *fill*\ …\ *end fill* specifier
set is used to input the elements of the array. A total of *N *\ entries
are required, where *N* = nx*ny.h](h/where }(hwhere h juhhh!NhNubj)}(h *arrayid*h]h/arrayid}(hhh juubah}(h]h]h]h]h]uhjh juubh// is a unique integer identifier for the array, }(h/ is a unique integer identifier for the array, h juhhh!NhNubj)}(h*nx*h]h/nx}(hhh juubah}(h]h]h]h]h]uhjh juubh/L is
the number of array elements moving left to right (i.e., columns), and
}(hL is
the number of array elements moving left to right (i.e., columns), and
h juhhh!NhNubj)}(h*ny*h]h/ny}(hhh juubah}(h]h]h]h]h]uhjh juubh/l is the number of array elements moving from bottom to top
(i.e., rows). The type of array is indicated by }(hl is the number of array elements moving from bottom to top
(i.e., rows). The type of array is indicated by h juhhh!NhNubj)}(h *aratype*h]h/aratype}(hhh juubah}(h]h]h]h]h]uhjh juubh/4 (e.g., square,
hexagonal). The optional parameter }(h4 (e.g., square,
hexagonal). The optional parameter h juhhh!NhNubj)}(h*pinpow*h]h/pinpow}(hhh jvubah}(h]h]h]h]h]uhjh juubh/ may be specified as either
}(h may be specified as either
h juhhh!NhNubj)}(h*yes*h]h/yes}(hhh j$vubah}(h]h]h]h]h]uhjh juubh/ or }(h or h juhhh!NhNubj)}(h*no*h]h/no}(hhh j7vubah}(h]h]h]h]h]uhjh juubh/_ (default is no) and is used to enable/disable pin power
edits for units within the array. The }(h_ (default is no) and is used to enable/disable pin power
edits for units within the array. The h juhhh!NhNubj)}(h*fill*h]h/fill}(hhh jJvubah}(h]h]h]h]h]uhjh juubh/ … }(h\ …\ h juhhh!NhNubj)}(h
*end fill*h]h/end fill}(hhh j]vubah}(h]h]h]h]h]uhjh juubh/F specifier
set is used to input the elements of the array. A total of }(hF specifier
set is used to input the elements of the array. A total of h juhhh!NhNubj)}(h&*N *\ entries
are required, where *N*h]h/$N * entries
are required, where *N}(hhh jpvubah}(h]h]h]h]h]uhjh juubh/ = nx*ny.}(h = nx*ny.h juhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM
h jhuhhubhM)}(h[Each of these portions of the array definition statement is described in
more detail below.h]h/[Each of these portions of the array definition statement is described in
more detail below.}(hjvh jvhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM
h jhuhhubh)}(h.. _9-2-3-9-1:h]h}(h]h]h]h]h]hid107uhh
hMh jhuhhh!h"ubh$)}(hhh](h))}(hArray typesh]h/Array types}(hjvh jvhhh!NhNubah}(h]h]h]h]h]uhh(h jvhhh!h"hMubhM)}(hXFNEWT supports arrays of cuboids, hexprisms, and rotated hexprism
elements. Four different array types may be selected. :numref:`tab9-2-2` lists
the supported array types and corresponding element types. The array
type given in the first column lists the keyword associated with each
type, as used in the typ= specifier; in some cases, multiple keywords
are associated with a specific array type. The element type in the
second column provides the boundary shape that can be used in the given
array type. For example, a cuboidal (square) array may only be filled
with cuboidal units.h](h/wNEWT supports arrays of cuboids, hexprisms, and rotated hexprism
elements. Four different array types may be selected. }(hwNEWT supports arrays of cuboids, hexprisms, and rotated hexprism
elements. Four different array types may be selected. h jvhhh!NhNubj)}(h:numref:`tab9-2-2`h]jM)}(hjvh]h/tab9-2-2}(hhh jvubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jvubah}(h]h]h]h]h]refdochj refdomainjvreftypenumrefrefexplicitrefwarnjWtab9-2-2uhjh!h"hMh jvubh/X lists
the supported array types and corresponding element types. The array
type given in the first column lists the keyword associated with each
type, as used in the typ= specifier; in some cases, multiple keywords
are associated with a specific array type. The element type in the
second column provides the boundary shape that can be used in the given
array type. For example, a cuboidal (square) array may only be filled
with cuboidal units.}(hX lists
the supported array types and corresponding element types. The array
type given in the first column lists the keyword associated with each
type, as used in the typ= specifier; in some cases, multiple keywords
are associated with a specific array type. The element type in the
second column provides the boundary shape that can be used in the given
array type. For example, a cuboidal (square) array may only be filled
with cuboidal units.h jvhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jvhhubh)}(h
.. _tab9-2-2:h]h}(h]h]h]h]h]htab9-2-2uhh
hMh jvhhh!h"ubj)}(hhh](h))}(h2NEWT array types with corresponding element types.h]h/2NEWT array types with corresponding element types.}(hjvh jvubah}(h]h]h]h]h]uhh(h!h"hMh jvubj)}(hhh](j)}(hhh]h}(h]h]h]h]h]colwidthKuhjh jwubj)}(hhh]h}(h]h]h]h]h]colwidthKuhjh jwubjh)}(hhh]j)}(hhh](j)}(hhh]hM)}(h**Array type**h]h)}(hj%wh]h/
Array type}(hhh j'wubah}(h]h]h]h]h]uhhh j#wubah}(h]h]h]h]h]uhhLh!h"hMh j wubah}(h]h]h]h]h]uhjh jwubj)}(hhh]hM)}(h**Element type**h]h)}(hjEwh]h/Element type}(hhh jGwubah}(h]h]h]h]h]uhhh jCwubah}(h]h]h]h]h]uhhLh!h"hMh j@wubah}(h]h]h]h]h]uhjh jwubeh}(h]h]h]h]h]uhjh jwubah}(h]h]h]h]h]uhjhh jwubj)}(hhh](j)}(hhh](j)}(hhh]hM)}(hCuboidal, squareh]h/Cuboidal, square}(hjwwh juwubah}(h]h]h]h]h]uhhLh!h"hMh jrwubah}(h]h]h]h]h]uhjh jowubj)}(hhh]hM)}(hCuboidh]h/Cuboid}(hjwh jwubah}(h]h]h]h]h]uhhLh!h"hMh jwubah}(h]h]h]h]h]uhjh jowubeh}(h]h]h]h]h]uhjh jlwubj)}(hhh](j)}(hhh]hM)}(hHexagonal, triangularh]h/Hexagonal, triangular}(hjwh jwubah}(h]h]h]h]h]uhhLh!h"hMh jwubah}(h]h]h]h]h]uhjh jwubj)}(hhh]hM)}(hHexprismh]h/Hexprism}(hjwh jwubah}(h]h]h]h]h]uhhLh!h"hMh jwubah}(h]h]h]h]h]uhjh jwubeh}(h]h]h]h]h]uhjh jlwubj)}(hhh](j)}(hhh]hM)}(h
Shexagonalh]h/
Shexagonal}(hjwh jwubah}(h]h]h]h]h]uhhLh!h"hMh jwubah}(h]h]h]h]h]uhjh jwubj)}(hhh]hM)}(hHexprismh]h/Hexprism}(hjwh jwubah}(h]h]h]h]h]uhhLh!h"hMh jwubah}(h]h]h]h]h]uhjh jwubeh}(h]h]h]h]h]uhjh jlwubj)}(hhh](j)}(hhh]hM)}(h
Rhexagonalh]h/
Rhexagonal}(hjxh jxubah}(h]h]h]h]h]uhhLh!h"hMh jxubah}(h]h]h]h]h]uhjh jxubj)}(hhh]hM)}(h Rhexprismh]h/ Rhexprism}(hj3xh j1xubah}(h]h]h]h]h]uhhLh!h"hMh j.xubah}(h]h]h]h]h]uhjh jxubeh}(h]h]h]h]h]uhjh jlwubeh}(h]h]h]h]h]uhjh jwubeh}(h]h]h]h]h]colsKuhjh jvubeh}(h](id196jveh]h]tab9-2-2ah]h]jEcenteruhjh jvhhh!h"hNj}j]xjvsj}jvjvsubhM)}(hXAll arrays are filled in a 2-D *i, j* pattern, with *i* varying from 1
to *nux* and *j* varying from 1 to *nuy*. All \ *nux*nuy* elements of
each array must be filled. :numref:`fig9-2-37` illustrates the layout of a
conceptual 4 by 4 cuboidal array, showing the row/column index for each
element of the array. :numref:`fig9-2-38` shows the row/column designation for
a 4 by 4 hexagonal array. Because of the shape of a hexprism, the array
itself is staggered. However, the row/column numbering is simple to
understand.h](h/All arrays are filled in a 2-D }(hAll arrays are filled in a 2-D h jcxhhh!NhNubj)}(h*i, j*h]h/i, j}(hhh jlxubah}(h]h]h]h]h]uhjh jcxubh/ pattern, with }(h pattern, with h jcxhhh!NhNubj)}(h*i*h]h/i}(hhh jxubah}(h]h]h]h]h]uhjh jcxubh/ varying from 1
to }(h varying from 1
to h jcxhhh!NhNubj)}(h*nux*h]h/nux}(hhh jxubah}(h]h]h]h]h]uhjh jcxubh/ and }(h and h jcxhhh!NhNubj)}(h*j*h]h/j}(hhh jxubah}(h]h]h]h]h]uhjh jcxubh/ varying from 1 to }(h varying from 1 to h jcxhhh!NhNubj)}(h*nuy*h]h/nuy}(hhh jxubah}(h]h]h]h]h]uhjh jcxubh/ . All }(h . All \ h jcxhhh!NhNubj)}(h *nux*nuy*h]h/nux*nuy}(hhh jxubah}(h]h]h]h]h]uhjh jcxubh/( elements of
each array must be filled. }(h( elements of
each array must be filled. h jcxhhh!NhNubj)}(h:numref:`fig9-2-37`h]jM)}(hjxh]h/ fig9-2-37}(hhh jxubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jxubah}(h]h]h]h]h]refdochj refdomainjxreftypenumrefrefexplicitrefwarnjW fig9-2-37uhjh!h"hM!h jcxubh/} illustrates the layout of a
conceptual 4 by 4 cuboidal array, showing the row/column index for each
element of the array. }(h} illustrates the layout of a
conceptual 4 by 4 cuboidal array, showing the row/column index for each
element of the array. h jcxhhh!NhNubj)}(h:numref:`fig9-2-38`h]jM)}(hjyh]h/ fig9-2-38}(hhh jyubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jyubah}(h]h]h]h]h]refdochj refdomainjyreftypenumrefrefexplicitrefwarnjW fig9-2-38uhjh!h"hM!h jcxubh/ shows the row/column designation for
a 4 by 4 hexagonal array. Because of the shape of a hexprism, the array
itself is staggered. However, the row/column numbering is simple to
understand.}(h shows the row/column designation for
a 4 by 4 hexagonal array. Because of the shape of a hexprism, the array
itself is staggered. However, the row/column numbering is simple to
understand.h jcxhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM!h jvhhubhM)}(hXThe stacked hexagon (shexagon) layout, as shown in :numref:`fig9-2-39`, was
developed to simply allow an alternate placement algorithm for
hexprisms. Any model that can be specified with *typ=hexagonal* can also
be specified with *type=shexagonal*; the choice of which form to use is
simply one of user preference. It is important to note that beginning
with row 3, units will be placed in a physical location different from
that of the hexagonal layout when the shexagonal layout is used.h](h/3The stacked hexagon (shexagon) layout, as shown in }(h3The stacked hexagon (shexagon) layout, as shown in h j.yhhh!NhNubj)}(h:numref:`fig9-2-39`h]jM)}(hj9yh]h/ fig9-2-39}(hhh j;yubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh j7yubah}(h]h]h]h]h]refdochj refdomainjEyreftypenumrefrefexplicitrefwarnjW fig9-2-39uhjh!h"hM*h j.yubh/u, was
developed to simply allow an alternate placement algorithm for
hexprisms. Any model that can be specified with }(hu, was
developed to simply allow an alternate placement algorithm for
hexprisms. Any model that can be specified with h j.yhhh!NhNubj)}(h*typ=hexagonal*h]h/
typ=hexagonal}(hhh j\yubah}(h]h]h]h]h]uhjh j.yubh/ can also
be specified with }(h can also
be specified with h j.yhhh!NhNubj)}(h*type=shexagonal*h]h/type=shexagonal}(hhh joyubah}(h]h]h]h]h]uhjh j.yubh/; the choice of which form to use is
simply one of user preference. It is important to note that beginning
with row 3, units will be placed in a physical location different from
that of the hexagonal layout when the shexagonal layout is used.}(h; the choice of which form to use is
simply one of user preference. It is important to note that beginning
with row 3, units will be placed in a physical location different from
that of the hexagonal layout when the shexagonal layout is used.h j.yhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM*h jvhhubhM)}(hXXFinally, the rotated hexprism (rhexprism) array is pictured in
:numref:`fig9-2-40`. This array is intended to facilitate placement of
rhexprisms. The numbering of cells is somewhat irregular because of the
staggered rows, but it is easy to follow if one is aware of the fill
pattern as illustrated in the figure. Note that the layout of a
rhexagonal array can be replicated exactly using a hexagonal or
rhexagonal array, placed in a hole, and rotated 90°. Thus, the type of
hexprism-based array used can always be tailored to the preferences of
the user and all can be used to create the same model.h](h/?Finally, the rotated hexprism (rhexprism) array is pictured in
}(h?Finally, the rotated hexprism (rhexprism) array is pictured in
h jyhhh!NhNubj)}(h:numref:`fig9-2-40`h]jM)}(hjyh]h/ fig9-2-40}(hhh jyubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jyubah}(h]h]h]h]h]refdochj refdomainjyreftypenumrefrefexplicitrefwarnjW fig9-2-40uhjh!h"hM2h jyubh/X. This array is intended to facilitate placement of
rhexprisms. The numbering of cells is somewhat irregular because of the
staggered rows, but it is easy to follow if one is aware of the fill
pattern as illustrated in the figure. Note that the layout of a
rhexagonal array can be replicated exactly using a hexagonal or
rhexagonal array, placed in a hole, and rotated 90°. Thus, the type of
hexprism-based array used can always be tailored to the preferences of
the user and all can be used to create the same model.}(hX. This array is intended to facilitate placement of
rhexprisms. The numbering of cells is somewhat irregular because of the
staggered rows, but it is easy to follow if one is aware of the fill
pattern as illustrated in the figure. Note that the layout of a
rhexagonal array can be replicated exactly using a hexagonal or
rhexagonal array, placed in a hole, and rotated 90°. Thus, the type of
hexprism-based array used can always be tailored to the preferences of
the user and all can be used to create the same model.h jyhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM2h jvhhubhM)}(hXMIt is often the case, especially for hexagonal-type arrays, that one
does not need to fill all array positions. While the array fill
procedure does require that all positions be filled, NEWT provides a
mechanism to fill a position with a null unit, effectively skipping that
position. This is discussed further under Fill Operations.h]h/XMIt is often the case, especially for hexagonal-type arrays, that one
does not need to fill all array positions. While the array fill
procedure does require that all positions be filled, NEWT provides a
mechanism to fill a position with a null unit, effectively skipping that
position. This is discussed further under Fill Operations.}(hjyh jyhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM<h jvhhubh)}(h.. _fig9-2-37:h]h}(h]h]h]h]h]h fig9-2-37uhh
hMBh jvhhh!h"ubj)}(hhh](j)}(he.. figure:: figs/NEWT/fig37.png
:align: center
:width: 400
Layout of a 4 by 4 cuboidal array.
h]h}(h]h]h]h]h]width400urifigs/NEWT/fig37.pngj*}j,jysuhjh jyh!h"hMGubj.)}(h"Layout of a 4 by 4 cuboidal array.h]h/"Layout of a 4 by 4 cuboidal array.}(hjyh jyubah}(h]h]h]h]h]uhj-h!h"hMGh jyubeh}(h](id197jyeh]h] fig9-2-37ah]h]jEcenteruhjhMGh jvhhh!h"j}jyjysj}jyjysubh)}(h.. _fig9-2-38:h]h}(h]h]h]h]h]h fig9-2-38uhh
hMIh jvhhh!h"ubj)}(hhh](j)}(hf.. figure:: figs/NEWT/fig38.png
:align: center
:width: 400
Layout of a 4 by 4 hexagonal array.
h]h}(h]h]h]h]h]width400urifigs/NEWT/fig38.pngj*}j,jzsuhjh jzh!h"hMNubj.)}(h#Layout of a 4 by 4 hexagonal array.h]h/#Layout of a 4 by 4 hexagonal array.}(hjzh jzubah}(h]h]h]h]h]uhj-h!h"hMNh jzubeh}(h](id198j
zeh]h] fig9-2-38ah]h]jEcenteruhjhMNh jvhhh!h"j}j0zjzsj}j
zjzsubh)}(h.. _fig9-2-39:h]h}(h]h]h]h]h]h fig9-2-39uhh
hMPh jvhhh!h"ubj)}(hhh](j)}(h{.. figure:: figs/NEWT/fig39.png
:align: center
:width: 400
Layout of a 4 by 4 stacked hexagonal (shexagonal) array.
h]h}(h]h]h]h]h]width400urifigs/NEWT/fig39.pngj*}j,jQzsuhjh jAzh!h"hMUubj.)}(h8Layout of a 4 by 4 stacked hexagonal (shexagonal) array.h]h/8Layout of a 4 by 4 stacked hexagonal (shexagonal) array.}(hjUzh jSzubah}(h]h]h]h]h]uhj-h!h"hMUh jAzubeh}(h](id199j@zeh]h] fig9-2-39ah]h]jEcenteruhjhMUh jvhhh!h"j}jfzj6zsj}j@zj6zsubh)}(h.. _fig9-2-40:h]h}(h]h]h]h]h]h fig9-2-40uhh
hMWh jvhhh!h"ubj)}(hhh](j)}(h{.. figure:: figs/NEWT/fig40.png
:align: center
:width: 400
Layout of a 4 by 4 rotated hexagonal (rhexagonal) array.
h]h}(h]h]h]h]h]width400urifigs/NEWT/fig40.pngj*}j,jzsuhjh jwzh!h"hM\ubj.)}(h8Layout of a 4 by 4 rotated hexagonal (rhexagonal) array.h]h/8Layout of a 4 by 4 rotated hexagonal (rhexagonal) array.}(hjzh jzubah}(h]h]h]h]h]uhj-h!h"hM\h jwzubeh}(h](id200jvzeh]h] fig9-2-40ah]h]jEcenteruhjhM\h jvhhh!h"j}jzjlzsj}jvzjlzsubhM)}(hXFAlthough all elements of cuboidal arrays **must** be cuboids, they need
not be the same size. Elements of each row must have the same height but
may have varying widths. Similarly, elements of each column must be of a
single common width but may vary in height. Less flexibility is
available in hex-based arrays, because of their very nature. Hexagonal
and stacked hexagonal arrays may contain only hexprisms, and all must be
of the same outer size (although unit contents may vary as needed).
Rotated hexagonal arrays likewise are limited to rhexprisms with a
single boundary size.h](h/)Although all elements of cuboidal arrays }(h)Although all elements of cuboidal arrays h jzhhh!NhNubh)}(h**must**h]h/must}(hhh jzubah}(h]h]h]h]h]uhhh jzubh/X be cuboids, they need
not be the same size. Elements of each row must have the same height but
may have varying widths. Similarly, elements of each column must be of a
single common width but may vary in height. Less flexibility is
available in hex-based arrays, because of their very nature. Hexagonal
and stacked hexagonal arrays may contain only hexprisms, and all must be
of the same outer size (although unit contents may vary as needed).
Rotated hexagonal arrays likewise are limited to rhexprisms with a
single boundary size.}(hX be cuboids, they need
not be the same size. Elements of each row must have the same height but
may have varying widths. Similarly, elements of each column must be of a
single common width but may vary in height. Less flexibility is
available in hex-based arrays, because of their very nature. Hexagonal
and stacked hexagonal arrays may contain only hexprisms, and all must be
of the same outer size (although unit contents may vary as needed).
Rotated hexagonal arrays likewise are limited to rhexprisms with a
single boundary size.h jzhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM^h jvhhubh)}(h.. _9-2-3-9-2:h]h}(h]h]h]h]h]hid108uhh
hMhh jvhhh!h"ubeh}(h](array-typesjveh]h](array types 9-2-3-9-1eh]h]uhh#h jhuhhh!h"hMj}jzjvsj}jvjvsubh$)}(hhh](h))}(hPin-power editsh]h/Pin-power edits}(hjzh jzhhh!NhNubah}(h]h]h]h]h]uhh(h jzhhh!h"hMkubhM)}(hXIn lattice-physics calculations, it is often necessary to obtain a
pin-power edit showing the power produced in each fuel pin cell. NEWT
uses the array functionality to define pin cells. When *pinpow=yes* is
specified, an extra edit is produced that gives the normalized pin power
in each pin cell. A pin cell is defined as any element within the array
that contains a fissionable nuclide. Pin powers are normalized such that
the average of all fuel-bearing array elements is 1.0. Array elements
such as burnable poison rods or water holes, which produce no *fission*
power, are not included in the power normalization process. The *pinpow*
functionality is not available for hexagonal, shexagonal, or rhexagonal
lattices.h](h/In lattice-physics calculations, it is often necessary to obtain a
pin-power edit showing the power produced in each fuel pin cell. NEWT
uses the array functionality to define pin cells. When }(hIn lattice-physics calculations, it is often necessary to obtain a
pin-power edit showing the power produced in each fuel pin cell. NEWT
uses the array functionality to define pin cells. When h jzhhh!NhNubj)}(h*pinpow=yes*h]h/
pinpow=yes}(hhh jzubah}(h]h]h]h]h]uhjh jzubh/Xb is
specified, an extra edit is produced that gives the normalized pin power
in each pin cell. A pin cell is defined as any element within the array
that contains a fissionable nuclide. Pin powers are normalized such that
the average of all fuel-bearing array elements is 1.0. Array elements
such as burnable poison rods or water holes, which produce no }(hXb is
specified, an extra edit is produced that gives the normalized pin power
in each pin cell. A pin cell is defined as any element within the array
that contains a fissionable nuclide. Pin powers are normalized such that
the average of all fuel-bearing array elements is 1.0. Array elements
such as burnable poison rods or water holes, which produce no h jzhhh!NhNubj)}(h *fission*h]h/fission}(hhh j{ubah}(h]h]h]h]h]uhjh jzubh/A
power, are not included in the power normalization process. The }(hA
power, are not included in the power normalization process. The h jzhhh!NhNubj)}(h*pinpow*h]h/pinpow}(hhh j{ubah}(h]h]h]h]h]uhjh jzubh/R
functionality is not available for hexagonal, shexagonal, or rhexagonal
lattices.}(hR
functionality is not available for hexagonal, shexagonal, or rhexagonal
lattices.h jzhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMmh jzhhubhM)}(hOutput provides an edit of each assembly for which *pinpow=yes* is
specified. In addition, a final edit is provided for the entire system,
normalized to all fuel cells in all arrays for which *pinpow=ye*\ s is
specified.h](h/3Output provides an edit of each assembly for which }(h3Output provides an edit of each assembly for which h j3{hhh!NhNubj)}(h*pinpow=yes*h]h/
pinpow=yes}(hhh j<{ubah}(h]h]h]h]h]uhjh j3{ubh/ is
specified. In addition, a final edit is provided for the entire system,
normalized to all fuel cells in all arrays for which }(h is
specified. In addition, a final edit is provided for the entire system,
normalized to all fuel cells in all arrays for which h j3{hhh!NhNubj)}(h*pinpow=ye*h]h/ pinpow=ye}(hhh jO{ubah}(h]h]h]h]h]uhjh j3{ubh/ s is
specified.}(h\ s is
specified.h j3{hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMyh jzhhubhM)}(hGPin-power edits are shown in the description of output in :ref:`9-2-5`.h](h/:Pin-power edits are shown in the description of output in }(h:Pin-power edits are shown in the description of output in h jh{hhh!NhNubj)}(h:ref:`9-2-5`h]j)}(hjs{h]h/9-2-5}(hhh ju{ubah}(h]h](jEstdstd-refeh]h]h]uhjh jq{ubah}(h]h]h]h]h]refdochj refdomainj{reftyperefrefexplicitrefwarnjW9-2-5uhjh!h"hM~h jh{ubh/.}(hhh jh{hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM~h jzhhubh)}(h.. _9-2-3-9-3:h]h}(h]h]h]h]h]hid109uhh
hMh jzhhh!h"ubeh}(h](pin-power-editsjzeh]h] 9-2-3-9-2ah]pin-power editsah]uhh#h jhuhhh!h"hMkjKj}j{jzsj}jzjzsubh$)}(hhh](h))}(hFill operationsh]h/Fill operations}(hj{h j{hhh!NhNubah}(h]h]h]h]h]uhh(h j{hhh!h"hMubhM)}(hX:The final section of an array specification is the *fill* list.
Delimited by *fill* and *end fill* keywords, NEWT expects a list of
N=nux*nuy unit numbers, specifying the unit to be placed at each array
position. Arrays are filled left to right, starting at the bottom
left-hand corner and moving up a row after all columns in the current
row are filled. In other words, any of the 4 × 4 arrays in the figures
above would be filled in the following order: (1,1), (2,1), (3,1),
(4,1), (1,2), (2,2), (3,2), (4,2), (1,3), (2,3), (3,3), (4,3), (1,4),
(2,4), (3,4), (4,4).h](h/3The final section of an array specification is the }(h3The final section of an array specification is the h j{hhh!NhNubj)}(h*fill*h]h/fill}(hhh j{ubah}(h]h]h]h]h]uhjh j{ubh/ list.
Delimited by }(h list.
Delimited by h j{hhh!NhNubj)}(h*fill*h]h/fill}(hhh j{ubah}(h]h]h]h]h]uhjh j{ubh/ and }(h and h j{hhh!NhNubj)}(h
*end fill*h]h/end fill}(hhh j{ubah}(h]h]h]h]h]uhjh j{ubh/X keywords, NEWT expects a list of
N=nux*nuy unit numbers, specifying the unit to be placed at each array
position. Arrays are filled left to right, starting at the bottom
left-hand corner and moving up a row after all columns in the current
row are filled. In other words, any of the 4 × 4 arrays in the figures
above would be filled in the following order: (1,1), (2,1), (3,1),
(4,1), (1,2), (2,2), (3,2), (4,2), (1,3), (2,3), (3,3), (4,3), (1,4),
(2,4), (3,4), (4,4).}(hX keywords, NEWT expects a list of
N=nux*nuy unit numbers, specifying the unit to be placed at each array
position. Arrays are filled left to right, starting at the bottom
left-hand corner and moving up a row after all columns in the current
row are filled. In other words, any of the 4 × 4 arrays in the figures
above would be filled in the following order: (1,1), (2,1), (3,1),
(4,1), (1,2), (2,2), (3,2), (4,2), (1,3), (2,3), (3,3), (4,3), (1,4),
(2,4), (3,4), (4,4).h j{hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j{hhubhM)}(hXThe list of elements used to fill an array consists of unit numbers.
Each unit used in the fill list must be defined in the geometry block
and must be of the shape and size required for the array type and
position. However, NEWT provides the ability to fill an array location
with a null unit, which in essence skips the current array location.
This is accomplished simply by entering unit number “0” (a “null” unit)
at the location to be skipped.h]h/XThe list of elements used to fill an array consists of unit numbers.
Each unit used in the fill list must be defined in the geometry block
and must be of the shape and size required for the array type and
position. However, NEWT provides the ability to fill an array location
with a null unit, which in essence skips the current array location.
This is accomplished simply by entering unit number “0” (a “null” unit)
at the location to be skipped.}(hj|h j
|hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh j{hhubh)}(h.. _9-2-3-9-4:h]h}(h]h]h]h]h]hid110uhh
hMh j{hhh!h"ubeh}(h](fill-operationsj{eh]h](fill operations 9-2-3-9-3eh]h]uhh#h jhuhhh!h"hMj}j)|j{sj}j{j{subh$)}(hhh](h))}(hExamples of array definitionsh]h/Examples of array definitions}(hj3|h j1|hhh!NhNubah}(h]h]h]h]h]uhh(h j.|hhh!h"hMubhM)}(hConsider a simple 3 × 3 square array with array ID 10, with unit 1 to be
placed in the center of the array, surrounded by unit 2 cells. Such a
specification would take the following form:h]h/Consider a simple 3 × 3 square array with array ID 10, with unit 1 to be
placed in the center of the array, surrounded by unit 2 cells. Such a
specification would take the following form:}(hjA|h j?|hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh j.|hhubjH)}(h@ara=10 nux=3 nuy=3 type=cuboidal fill 2 2 2 2 1 2 2 2 2 end fillh]h/@ara=10 nux=3 nuy=3 type=cuboidal fill 2 2 2 2 1 2 2 2 2 end fill}(hhh jM|ubah}(h]h]h]h]h]j=j>uhjGh!h"hMh j.|hhubhM)}(hMThis may also be written spanning several lines to help visualize the layout:h]h/MThis may also be written spanning several lines to help visualize the layout:}(hj]|h j[|hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh j.|hhubjH)}(h@ara=10 nux=3 nuy=3 type=cuboidal fill
2 2 2
2 1 2
2 2 2 end fillh]h/@ara=10 nux=3 nuy=3 type=cuboidal fill
2 2 2
2 1 2
2 2 2 end fill}(hhh ji|ubah}(h]h]h]h]h]j=j>uhjGh!h"hMh j.|hhubhM)}(hXJNote that the array is being filled from the bottom so that the actual unit
layout is inverted relative to the fill description. A fill specification that
places unit 1 at the top center position in this array would be input as
follows, where the second-to-last entry in the list is placed in the horizontal
center of the top row.h]h/XJNote that the array is being filled from the bottom so that the actual unit
layout is inverted relative to the fill description. A fill specification that
places unit 1 at the top center position in this array would be input as
follows, where the second-to-last entry in the list is placed in the horizontal
center of the top row.}(hjy|h jw|hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh j.|hhubjH)}(h@ara=10 nux=3 nuy=3 type=cuboidal fill
2 2 2
2 1 2
2 1 2 end fillh]h/@ara=10 nux=3 nuy=3 type=cuboidal fill
2 2 2
2 1 2
2 1 2 end fill}(hhh j|ubah}(h]h]h]h]h]j=j>uhjGh!h"hMh j.|hhubhM)}(hArrays may be nested within arrays. Each array must be placed in a unit, but a
unit containing an array may be placed within another array. The following
example demonstrates the use of nested arrays, along with the use of a null
unit.h]h/Arrays may be nested within arrays. Each array must be placed in a unit, but a
unit containing an array may be placed within another array. The following
example demonstrates the use of nested arrays, along with the use of a null
unit.}(hj|h j|hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh j.|hhubhM)}(hIn this example, we define two units containing cells, a unit containing a
smaller array and a global unit containing a larger array:h]h/In this example, we define two units containing cells, a unit containing a
smaller array and a global unit containing a larger array:}(hj|h j|hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh j.|hhubjH)}(hX'unit 1
'0.5/0.6 cm radius pin
cylinder 30 0.5 sides=20
cylinder 20 0.6 sides=20
cuboid 10 4p0.75
media 1 1 30
media 2 1 20 -30
media 3 1 10 -20
boundary 10 3 3
unit 2
'0.25/0.3 cm radius pin
cylinder 30 0.25 sides=8
cylinder 20 0.3 sides=8
cuboid 10 4p0.375
media 1 1 30
media 2 1 20 -30
media 3 1 10 -20
boundary 10 3 3
'small array
unit 3
cuboid 10 1.5 0 1.5 0
array 1 10 place 1 1 0.375 0.375
media 3 1 10
boundary 10 5 5 'large array
global unit 4
cuboid 10 3.0 0.0 3.0 0.0
array 2 10 place 1 1 0.75 0.75
media 3 1 10
boundary 10 5 5h]h/X'unit 1
'0.5/0.6 cm radius pin
cylinder 30 0.5 sides=20
cylinder 20 0.6 sides=20
cuboid 10 4p0.75
media 1 1 30
media 2 1 20 -30
media 3 1 10 -20
boundary 10 3 3
unit 2
'0.25/0.3 cm radius pin
cylinder 30 0.25 sides=8
cylinder 20 0.3 sides=8
cuboid 10 4p0.375
media 1 1 30
media 2 1 20 -30
media 3 1 10 -20
boundary 10 3 3
'small array
unit 3
cuboid 10 1.5 0 1.5 0
array 1 10 place 1 1 0.375 0.375
media 3 1 10
boundary 10 5 5 'large array
global unit 4
cuboid 10 3.0 0.0 3.0 0.0
array 2 10 place 1 1 0.75 0.75
media 3 1 10
boundary 10 5 5}(hhh j|ubah}(h]h]h]h]h]forcehighlight_args}j=j>languagenoneuhjGh!h"hMh j.|hhubhM)}(hNow, in a *read array* block, we define array 1, a 2 by 2 array filled
with unit 2 cells, and array 2, filled with two unit 1 cells, one unit 3
cell (containing array 1), and one null unit:h](h/
Now, in a }(h
Now, in a h j|hhh!NhNubj)}(h*read array*h]h/
read array}(hhh j|ubah}(h]h]h]h]h]uhjh j|ubh/ block, we define array 1, a 2 by 2 array filled
with unit 2 cells, and array 2, filled with two unit 1 cells, one unit 3
cell (containing array 1), and one null unit:}(h block, we define array 1, a 2 by 2 array filled
with unit 2 cells, and array 2, filled with two unit 1 cells, one unit 3
cell (containing array 1), and one null unit:h j|hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j.|hhubjH)}(hread array
ara=1 nux=2 nuy=2 typ=cuboidal
fill 2 2
2 2 end fill
'
ara=2 nux=2 nuy=2 typ=cuboidal
fill 1 3
0 1 end fill
end arrayh]h/read array
ara=1 nux=2 nuy=2 typ=cuboidal
fill 2 2
2 2 end fill
'
ara=2 nux=2 nuy=2 typ=cuboidal
fill 1 3
0 1 end fill
end array}(hhh j|ubah}(h]h]h]h]h]j=j>uhjGh!h"hMh j.|hhubhM)}(hWhen assembled, the model would appear as shown in :numref:`fig9-2-41`. Note
that local grids override the global grid in each array location but
that the global grid is seen where the null unit is placed.h](h/3When assembled, the model would appear as shown in }(h3When assembled, the model would appear as shown in h j|hhh!NhNubj)}(h:numref:`fig9-2-41`h]jM)}(hj|h]h/ fig9-2-41}(hhh j|ubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh j|ubah}(h]h]h]h]h]refdochj refdomainj }reftypenumrefrefexplicitrefwarnjW fig9-2-41uhjh!h"hMh j|ubh/. Note
that local grids override the global grid in each array location but
that the global grid is seen where the null unit is placed.}(h. Note
that local grids override the global grid in each array location but
that the global grid is seen where the null unit is placed.h j|hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j.|hhubh)}(h.. _fig9-2-41:h]h}(h]h]h]h]h]h fig9-2-41uhh
hMh j.|hhh!h"ubj)}(hhh](j)}(hz.. figure:: figs/NEWT/fig41.png
:align: center
:width: 500
Example of nested arrays and a null unit specification.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig41.pngj*}j,jA}suhjh j1}h!h"hMubj.)}(h7Example of nested arrays and a null unit specification.h]h/7Example of nested arrays and a null unit specification.}(hjE}h jC}ubah}(h]h]h]h]h]uhj-h!h"hMh j1}ubeh}(h](id201j0}eh]h] fig9-2-41ah]h]jEcenteruhjhMh j.|hhh!h"j}jV}j&}sj}j0}j&}subh)}(h
.. _9-2-3-10:h]h}(h]h]h]h]h]hid111uhh
hMh j.|hhh!h"ubeh}(h](examples-of-array-definitionsj"|eh]h](examples of array definitions 9-2-3-9-4eh]h]uhh#h jhuhhh!h"hMj}jm}j|sj}j"|j|subeh}(h](array-definitionjIueh]h](array definition9-2-3-9eh]h]uhh#h jhhh!h"hM
j}jx}j?usj}jIuj?usubh$)}(hhh](h))}(hHomogenization blockh]h/Homogenization block}(hj}h j}hhh!NhNubah}(h]h]h]h]h]uhh(h j}}hhh!h"hMubhM)}(h4**Homogenization block keyword = homog, hmog, homo**h]h)}(hj}h]h/0Homogenization block keyword = homog, hmog, homo}(hhh j}ubah}(h]h]h]h]h]uhhh j}ubah}(h]h]h]h]h]uhhLh!h"hMh j}}hhubhM)}(hXAs discussed earlier, NEWT can be used to collapse cross sections to a
reduced broad-group format. The cross sections produced from this
operation are written as microscopic cross sections for each nuclide in
each mixture. NEWT also provides the ability to produce macroscopic
weighted cross sections homogenized over one or more mixtures.
Homogenized cross sections are created using the collapsing energy
structure defined in the collapse data block or the original library’s
group structure if no collapsing instructions are provided.
Flux-weighted collapsed cross sections are combined with number
densities and added such that reaction rates in homogenized materials
are conserved.h]h/XAs discussed earlier, NEWT can be used to collapse cross sections to a
reduced broad-group format. The cross sections produced from this
operation are written as microscopic cross sections for each nuclide in
each mixture. NEWT also provides the ability to produce macroscopic
weighted cross sections homogenized over one or more mixtures.
Homogenized cross sections are created using the collapsing energy
structure defined in the collapse data block or the original library’s
group structure if no collapsing instructions are provided.
Flux-weighted collapsed cross sections are combined with number
densities and added such that reaction rates in homogenized materials
are conserved.}(hj}h j}hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM h j}}hhubhM)}(hXWithin the homogenization block, multiple homogenization records are
permitted, and the same mixtures may be repeated in different records.
Each record provides a recipe defining the mixtures to be homogenized.
Homogenization records have the following form:h]h/XWithin the homogenization block, multiple homogenization records are
permitted, and the same mixtures may be repeated in different records.
Each record provides a recipe defining the mixtures to be homogenized.
Homogenization records have the following form:}(hj}h j}hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh j}}hhubjH)}(h\Homogenized Mixture List of end
Mixture ID Description Mixturesh]h/\Homogenized Mixture List of end
Mixture ID Description Mixtures}(hhh j}ubah}(h]h]h]h]h]j=j>uhjGh!h"hMh j}}hhubhM)}(hXzThe homogenized mixture ID is the “nuclide” number under which the
mixture is saved on the homogenized cross section library. The value is
arbitrary and serves only as a means to identify the cross section set
on the library, although each ID must be unique. The mixture description
is an alphanumeric label of up to 12 characters that is associated with
the mixture; this label provides a little more descriptive ability than
the ID itself. The label may not contain blanks. Finally, the label is
followed by the list of mixtures to be homogenized, terminated by the
end keyword. The list may contain up to 1000 unique mixtures.h]h/XzThe homogenized mixture ID is the “nuclide” number under which the
mixture is saved on the homogenized cross section library. The value is
arbitrary and serves only as a means to identify the cross section set
on the library, although each ID must be unique. The mixture description
is an alphanumeric label of up to 12 characters that is associated with
the mixture; this label provides a little more descriptive ability than
the ID itself. The label may not contain blanks. Finally, the label is
followed by the list of mixtures to be homogenized, terminated by the
end keyword. The list may contain up to 1000 unique mixtures.}(hj}h j}hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh j}}hhubhM)}(hXA sample homogenization block is shown below. In this illustration, two
homogenized mixtures are created. This first consists of five different
fuel mixtures (201–205); this could be used to obtain the average fuel
cross section for an assembly containing five different fuel types. The
homogenized cross sections will be written to the homogenized library as
nuclide 500, with label “fuel.” The second instruction homogenizes
mixtures 201, 210, and 220 from the original problem; this could be
used, for example, to homogenize the fuel, clad, and moderator of a fuel
pin cell. This cross section set would be written on the same library as
nuclide 501, with the label “fuel_cell201.”h]h/XA sample homogenization block is shown below. In this illustration, two
homogenized mixtures are created. This first consists of five different
fuel mixtures (201–205); this could be used to obtain the average fuel
cross section for an assembly containing five different fuel types. The
homogenized cross sections will be written to the homogenized library as
nuclide 500, with label “fuel.” The second instruction homogenizes
mixtures 201, 210, and 220 from the original problem; this could be
used, for example, to homogenize the fuel, clad, and moderator of a fuel
pin cell. This cross section set would be written on the same library as
nuclide 501, with the label “fuel_cell201.”}(hj}h j}hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM)h j}}hhubjH)}(h\read hmog
500 fuel 201 202 203 204 205 end
501 fuel_cell201 201 210 220 end
end hmogh]h/\read hmog
500 fuel 201 202 203 204 205 end
501 fuel_cell201 201 210 220 end
end hmog}(hhh j}ubah}(h]h]h]h]h]j=j>uhjGh!h"hM6h j}}hhubhM)}(hHomogenized (macroscopic) cross sections are saved in an AMPX
working-format library at the unit specified by the *hmoglib=* parameter
(default=13) [ft13f001].h](h/sHomogenized (macroscopic) cross sections are saved in an AMPX
working-format library at the unit specified by the }(hsHomogenized (macroscopic) cross sections are saved in an AMPX
working-format library at the unit specified by the h j}hhh!NhNubj)}(h
*hmoglib=*h]h/hmoglib=}(hhh j~ubah}(h]h]h]h]h]uhjh j}ubh/# parameter
(default=13) [ft13f001].}(h# parameter
(default=13) [ft13f001].h j}hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM;h j}}hhubh)}(h
.. _9-2-3-11:h]h}(h]h]h]h]h]hid112uhh
hM?h j}}hhh!h"ubeh}(h](homogenization-blockjf}eh]h](homogenization block9-2-3-10eh]h]uhh#h jhhh!h"hMj}j,~j\}sj}jf}j\}subh$)}(hhh](h))}(hAssembly discontinuity factorsh]h/Assembly discontinuity factors}(hj6~h j4~hhh!NhNubah}(h]h]h]h]h]uhh(h j1~hhh!h"hMBubhM)}(h;**Assembly discontinuity factor (adf) block keyword = adf**h]h)}(hjD~h]h/7Assembly discontinuity factor (adf) block keyword = adf}(hhh jF~ubah}(h]h]h]h]h]uhhh jB~ubah}(h]h]h]h]h]uhhLh!h"hMDh j1~hhubhM)}(hXBecause discontinuity factors have meaning only with respect to
homogenized cross sections, ADFs are calculated only if homogenized
cross sections are also specified via the Homogenization data block
(see :ref:`9-2-3-10`). Calculation of ADFs is specified in the *read adf*
data block. The three supported formats of this data block are as
follows. For a single-assembly model, the following format is used:h](h/Because discontinuity factors have meaning only with respect to
homogenized cross sections, ADFs are calculated only if homogenized
cross sections are also specified via the Homogenization data block
(see }(hBecause discontinuity factors have meaning only with respect to
homogenized cross sections, ADFs are calculated only if homogenized
cross sections are also specified via the Homogenization data block
(see h jY~hhh!NhNubj)}(h:ref:`9-2-3-10`h]j)}(hjd~h]h/9-2-3-10}(hhh jf~ubah}(h]h](jEstdstd-refeh]h]h]uhjh jb~ubah}(h]h]h]h]h]refdochj refdomainjp~reftyperefrefexplicitrefwarnjW9-2-3-10uhjh!h"hMFh jY~ubh/+). Calculation of ADFs is specified in the }(h+). Calculation of ADFs is specified in the h jY~hhh!NhNubj)}(h
*read adf*h]h/read adf}(hhh j~ubah}(h]h]h]h]h]uhjh jY~ubh/
data block. The three supported formats of this data block are as
follows. For a single-assembly model, the following format is used:}(h
data block. The three supported formats of this data block are as
follows. For a single-assembly model, the following format is used:h jY~hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMFh j1~hhubjH)}(h3read adf
1 homg_assm_id n=Y1 s=Y2 e=X1 w=X2
end adfh]h/3read adf
1 homg_assm_id n=Y1 s=Y2 e=X1 w=X2
end adf}(hhh j~ubah}(h]h]h]h]h]j=j>uhjGh!h"hMOh j1~hhubhM)}(h=For a reflected assembly model, the following format is used:h]h/=For a reflected assembly model, the following format is used:}(hj~h j~hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMSh j1~hhubjH)}(h2read adf
2 homg_assm_id homog_refl_id w=Xi
end adfh]h/2read adf
2 homg_assm_id homog_refl_id w=Xi
end adf}(hhh j~ubah}(h]h]h]h]h]j=j>uhjGh!h"hMWh j1~hhubjH)}(h5read adf
3 homg_assm_id line1 line2 line3 ...
end adfh]h/5read adf
3 homg_assm_id line1 line2 line3 ...
end adf}(hhh j~ubah}(h]h]h]h]h]j=j>uhjGh!h"hM]h j1~hhubhM)}(hwhereh]h/where}(hj~h j~hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMah j1~hhubjP)}(hhh](jP)}(hhh](hM)}(hV``hmog_assm_id`` is the identifying label assigned to the homogenized assembly,h](jM)}(h``hmog_assm_id``h]h/hmog_assm_id}(hhh j~ubah}(h]h]h]h]h]uhjLh j~ubh/F is the identifying label assigned to the homogenized assembly,}(hF is the identifying label assigned to the homogenized assembly,h j~ubeh}(h]h]h]h]h]uhhLh!h"hMch j~ubjP)}(hhh]hM)}(hP``hmog_refl_id`` is the label assigned to the homogenized reflector region,h](jM)}(h``hmog_refl_id``h]h/hmog_refl_id}(hhh jubah}(h]h]h]h]h]uhjLh jubh/@ is the label assigned to the homogenized reflector region,}(h@ is the label assigned to the homogenized reflector region,h jubeh}(h]h]h]h]h]uhhLh!h"hMeh j ubah}(h]h]h]h]h]uhjOh j~ubeh}(h]h]h]h]h]uhjOh j~ubhM)}(hz``Y1`` is the y-ordinate of the north boundary of the assembly
(typically this is y\ :sub:`max` for the global unit),h](jM)}(h``Y1``h]h/Y1}(hhh j9ubah}(h]h]h]h]h]uhjLh j5ubh/T is the y-ordinate of the north boundary of the assembly
(typically this is y }(hT is the y-ordinate of the north boundary of the assembly
(typically this is y\ h j5ubj)}(h
:sub:`max`h]h/max}(hhh jLubah}(h]h]h]h]h]uhjh j5ubh/ for the global unit),}(h for the global unit),h j5ubeh}(h]h]h]h]h]uhhLh!h"hMgh j~ubhM)}(hz``Y2`` is the y-ordinate of the south boundary of the assembly (typically this is y\ :sub:`min` for the global unit),h](jM)}(h``Y2``h]h/Y2}(hhh jiubah}(h]h]h]h]h]uhjLh jeubh/T is the y-ordinate of the south boundary of the assembly (typically this is y }(hT is the y-ordinate of the south boundary of the assembly (typically this is y\ h jeubj)}(h
:sub:`min`h]h/min}(hhh j|ubah}(h]h]h]h]h]uhjh jeubh/ for the global unit),}(h for the global unit),h jeubeh}(h]h]h]h]h]uhhLh!h"hMjh j~ubhM)}(hy``X1`` is the x-ordinate of the east boundary of the assembly
(typically this is x\ :sub:`max` for the global unit),h](jM)}(h``X1``h]h/X1}(hhh jubah}(h]h]h]h]h]uhjLh jubh/S is the x-ordinate of the east boundary of the assembly
(typically this is x }(hS is the x-ordinate of the east boundary of the assembly
(typically this is x\ h jubj)}(h
:sub:`max`h]h/max}(hhh jubah}(h]h]h]h]h]uhjh jubh/ for the global unit),}(h for the global unit),h jubeh}(h]h]h]h]h]uhhLh!h"hMlh j~ubhM)}(hy``X2`` is the x-ordinate of the east boundary of the assembly
(typically this is x\ :sub:`max` for the global unit),h](jM)}(h``X2``h]h/X2}(hhh jubah}(h]h]h]h]h]uhjLh jubh/S is the x-ordinate of the east boundary of the assembly
(typically this is x }(hS is the x-ordinate of the east boundary of the assembly
(typically this is x\ h jubj)}(h
:sub:`max`h]h/max}(hhh jubah}(h]h]h]h]h]uhjh jubh/ for the global unit),}(h for the global unit),h jubeh}(h]h]h]h]h]uhhLh!h"hMoh j~ubhM)}(h?``Xi`` is the x-ordinate for the fuel/reflector interface,h](jM)}(h``Xi``h]h/Xi}(hhh jubah}(h]h]h]h]h]uhjLh jubh/9 is the x-ordinate for the fuel/reflector interface,}(h9 is the x-ordinate for the fuel/reflector interface,h jubeh}(h]h]h]h]h]uhhLh!h"hMrh j~ubhM)}(hy``linei`` is a series of two ordered pairs (``X1``,``Y2``), (``X1``,``Y2``)that define a line segment in the NEWT grid.h](jM)}(h ``linei``h]h/linei}(hhh jubah}(h]h]h]h]h]uhjLh jubh/% is a series of two ordered pairs (}(h% is a series of two ordered pairs (h jubjM)}(h``X1``h]h/X1}(hhh j)ubah}(h]h]h]h]h]uhjLh jubh/,``Y2``), (}(h,``Y2``), (h jubjM)}(h``X1``h]h/X1}(hhh j<ubah}(h]h]h]h]h]uhjLh jubh/4,``Y2``)that define a line segment in the NEWT grid.}(h4,``Y2``)that define a line segment in the NEWT grid.h jubeh}(h]h]h]h]h]uhhLh!h"hMth j~ubeh}(h]h]h]h]h]uhjOh j1~hhh!h"hNubhM)}(hXIn a single-assembly calculation, only a single homogenized mixture is
specified. Leading index 1 indicates that ADFs for the fuel assembly are
being calculated; ADFs may be calculated on any or all faces of a
rectangular assembly. In a reflected assembly, the leading index is 2,
followed by the homogenized mixture ID for the fuel assembly first, then
the homogenized mixture ID for the reflector region. An ADF may be
requested only for one location, at the fuel/reflector interface. In any
configuration, ADFs may be requested for a set of arbitrary line
segments defined in the NEWT geometry. In this case, the leading index
is 3, followed by the homogenized mixture ID, followed by up to 12 line
segments, which are defined by their beginning and ending points. ADFs
along these lines are defined as the surface-averaged flux divided by
the average flux defined for the associated homogenized mixture.
Surface-averaged currents are also edited for each arbitrary line
segment; both full and partial currents in both the x- and y- directions
are provided. The net current is also provided in the few-group cross
section database file *xfile016*. The orientation of the net current
across the line segment is further discussed in Appendix A of TRITON
chapter.h](h/XtIn a single-assembly calculation, only a single homogenized mixture is
specified. Leading index 1 indicates that ADFs for the fuel assembly are
being calculated; ADFs may be calculated on any or all faces of a
rectangular assembly. In a reflected assembly, the leading index is 2,
followed by the homogenized mixture ID for the fuel assembly first, then
the homogenized mixture ID for the reflector region. An ADF may be
requested only for one location, at the fuel/reflector interface. In any
configuration, ADFs may be requested for a set of arbitrary line
segments defined in the NEWT geometry. In this case, the leading index
is 3, followed by the homogenized mixture ID, followed by up to 12 line
segments, which are defined by their beginning and ending points. ADFs
along these lines are defined as the surface-averaged flux divided by
the average flux defined for the associated homogenized mixture.
Surface-averaged currents are also edited for each arbitrary line
segment; both full and partial currents in both the x- and y- directions
are provided. The net current is also provided in the few-group cross
section database file }(hXtIn a single-assembly calculation, only a single homogenized mixture is
specified. Leading index 1 indicates that ADFs for the fuel assembly are
being calculated; ADFs may be calculated on any or all faces of a
rectangular assembly. In a reflected assembly, the leading index is 2,
followed by the homogenized mixture ID for the fuel assembly first, then
the homogenized mixture ID for the reflector region. An ADF may be
requested only for one location, at the fuel/reflector interface. In any
configuration, ADFs may be requested for a set of arbitrary line
segments defined in the NEWT geometry. In this case, the leading index
is 3, followed by the homogenized mixture ID, followed by up to 12 line
segments, which are defined by their beginning and ending points. ADFs
along these lines are defined as the surface-averaged flux divided by
the average flux defined for the associated homogenized mixture.
Surface-averaged currents are also edited for each arbitrary line
segment; both full and partial currents in both the x- and y- directions
are provided. The net current is also provided in the few-group cross
section database file h j[hhh!NhNubj)}(h
*xfile016*h]h/xfile016}(hhh jdubah}(h]h]h]h]h]uhjh j[ubh/r. The orientation of the net current
across the line segment is further discussed in Appendix A of TRITON
chapter.}(hr. The orientation of the net current
across the line segment is further discussed in Appendix A of TRITON
chapter.h j[hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMvh j1~hhubhM)}(hXVAlthough any homogenized set of mixtures can be specified for each
homogenized region, the ADF will have physical meaning only if the
homogenized set represents all mixtures in the assembly. Similarly, if a
reflector calculation is performed, the *hmog_refl_id* should represent
the set of homogenized reflector mixtures. The average collapsed flux in
the homogenized mixtures is used to calculate the homogeneous flux for a
single-assembly ADF. In a reflector calculation, the homogenized
cross sections for the reflector are used to solve the multigroup
diffusion approximation (:ref:`9-2-2-5`).h](h/Although any homogenized set of mixtures can be specified for each
homogenized region, the ADF will have physical meaning only if the
homogenized set represents all mixtures in the assembly. Similarly, if a
reflector calculation is performed, the }(hAlthough any homogenized set of mixtures can be specified for each
homogenized region, the ADF will have physical meaning only if the
homogenized set represents all mixtures in the assembly. Similarly, if a
reflector calculation is performed, the h j}hhh!NhNubj)}(h*hmog_refl_id*h]h/hmog_refl_id}(hhh jubah}(h]h]h]h]h]uhjh j}ubh/XA should represent
the set of homogenized reflector mixtures. The average collapsed flux in
the homogenized mixtures is used to calculate the homogeneous flux for a
single-assembly ADF. In a reflector calculation, the homogenized
cross sections for the reflector are used to solve the multigroup
diffusion approximation (}(hXA should represent
the set of homogenized reflector mixtures. The average collapsed flux in
the homogenized mixtures is used to calculate the homogeneous flux for a
single-assembly ADF. In a reflector calculation, the homogenized
cross sections for the reflector are used to solve the multigroup
diffusion approximation (h j}hhh!NhNubj)}(h:ref:`9-2-2-5`h]j)}(hjh]h/9-2-2-5}(hhh jubah}(h]h](jEstdstd-refeh]h]h]uhjh jubah}(h]h]h]h]h]refdochj refdomainjreftyperefrefexplicitrefwarnjW9-2-2-5uhjh!h"hMh j}ubh/).}(h).h j}hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j1~hhubhM)}(hX:Examples illustrate the use of the ADF input specification. Consider a
17 × 17 pressurized-water-reactor (PWR) design. Because of symmetry, it
can be modeled a ¼ assembly; therefore, we choose to model the upper
right quadrant, as shown in :numref:`fig9-2-42`. Mixtures 1, 2, 3, and 4
represent the fuel, clad, moderator, and guide tube materials,
respectively. The west and south sides of the model are the assembly
midplanes, so ADFs calculated on these boundaries would have no physical
meaning. (These are not real assembly boundaries.) However, because of
the symmetry of the assembly, fluxes would be identical on all
boundaries. Therefore, selection of either the north or east boundary
will yield a valid ADF for all boundaries. We choose to request an ADF
calculation for the east (right) side of the assembly.h](h/Examples illustrate the use of the ADF input specification. Consider a
17 × 17 pressurized-water-reactor (PWR) design. Because of symmetry, it
can be modeled a ¼ assembly; therefore, we choose to model the upper
right quadrant, as shown in A}(hExamples illustrate the use of the ADF input specification. Consider a
17 × 17 pressurized-water-reactor (PWR) design. Because of symmetry, it
can be modeled a ¼ assembly; therefore, we choose to model the upper
right quadrant, as shown in h jĀhhh!NhNubj)}(h:numref:`fig9-2-42`h]jM)}(hjπh]h/ fig9-2-42}(hhh jрubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh j̀ubah}(h]h]h]h]h]refdochj refdomainjۀreftypenumrefrefexplicitrefwarnjW fig9-2-42uhjh!h"hMh jĀubh/X1. Mixtures 1, 2, 3, and 4
represent the fuel, clad, moderator, and guide tube materials,
respectively. The west and south sides of the model are the assembly
midplanes, so ADFs calculated on these boundaries would have no physical
meaning. (These are not real assembly boundaries.) However, because of
the symmetry of the assembly, fluxes would be identical on all
boundaries. Therefore, selection of either the north or east boundary
will yield a valid ADF for all boundaries. We choose to request an ADF
calculation for the east (right) side of the assembly.}(hX1. Mixtures 1, 2, 3, and 4
represent the fuel, clad, moderator, and guide tube materials,
respectively. The west and south sides of the model are the assembly
midplanes, so ADFs calculated on these boundaries would have no physical
meaning. (These are not real assembly boundaries.) However, because of
the symmetry of the assembly, fluxes would be identical on all
boundaries. Therefore, selection of either the north or east boundary
will yield a valid ADF for all boundaries. We choose to request an ADF
calculation for the east (right) side of the assembly.h jĀhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j1~hhubh)}(h.. _fig9-2-42:h]h}(h]h]h]h]h]h fig9-2-42uhh
hMh j1~hhh!h"ubj)}(hhh](j)}(hw.. figure:: figs/NEWT/fig42.png
:align: center
:width: 400
Upper-right quadrant of an unreflected PWR assembly.
h]h}(h]h]h]h]h]width400urifigs/NEWT/fig42.pngj*}j,jsuhjh jh!h"hMubj.)}(h4Upper-right quadrant of an unreflected PWR assembly.h]h/4Upper-right quadrant of an unreflected PWR assembly.}(hjh jubah}(h]h]h]h]h]uhj-h!h"hMh jubeh}(h](id202jeh]h] fig9-2-42ah]h]jEcenteruhjhMh j1~hhh!h"j}j(jsj}jjsubhM)}(hAssuming we are collapsing 44 energy groups to 2 energy groups, we would
specify the following *collapse*, *homog*, and *adf* blocks to obtain
2-group ADFs representative of this assembly:h](h/_Assuming we are collapsing 44 energy groups to 2 energy groups, we would
specify the following }(h_Assuming we are collapsing 44 energy groups to 2 energy groups, we would
specify the following h j.hhh!NhNubj)}(h
*collapse*h]h/collapse}(hhh j7ubah}(h]h]h]h]h]uhjh j.ubh/, }(h, h j.hhh!NhNubj)}(h*homog*h]h/homog}(hhh jJubah}(h]h]h]h]h]uhjh j.ubh/, and }(h, and h j.hhh!NhNubj)}(h*adf*h]h/adf}(hhh j]ubah}(h]h]h]h]h]uhjh j.ubh/? blocks to obtain
2-group ADFs representative of this assembly:}(h? blocks to obtain
2-group ADFs representative of this assembly:h j.hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j1~hhubjH)}(hnread collapse
22r1 22r2
end collapse
read hmog
500 assm 1 2 3 4 end
end hmog
read adf
1 500 e=10.752
end adfh]h/nread collapse
22r1 22r2
end collapse
read hmog
500 assm 1 2 3 4 end
end hmog
read adf
1 500 e=10.752
end adf}(hhh jvubah}(h]h]h]h]h]j=j>uhjGh!h"hMh j1~hhubhM)}(hAgain, recall that for a single assembly, the ADF in each energy group
is simply the average flux on the specified boundary divided by the
average flux for the entire assembly, which in this case is the flux in
homogenized mixture 500.h]h/Again, recall that for a single assembly, the ADF in each energy group
is simply the average flux on the specified boundary divided by the
average flux for the entire assembly, which in this case is the flux in
homogenized mixture 500.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh j1~hhubhM)}(hADF can also be calculated using the arbitrary line-segment ADF type.
Using this new ADF type, the ADF input would be the following:h]h/ADF can also be calculated using the arbitrary line-segment ADF type.
Using this new ADF type, the ADF input would be the following:}(hjh jhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh j1~hhubjH)}(h~read collapse
22r1 22r2
end collapse
read hmog
500 assm 1 2 3 4 end
end hmog
read adf
3 500 10.752 0.0 10.752 10.752
end adfh]h/~read collapse
22r1 22r2
end collapse
read hmog
500 assm 1 2 3 4 end
end hmog
read adf
3 500 10.752 0.0 10.752 10.752
end adf}(hhh jubah}(h]h]h]h]h]j=j>uhjGh!h"hMh j1~hhubhM)}(hIn this example, the east-side ADF will be calculated along the line
segment starting at (10.752,0) and ending at (10.752,10.752). The values
of the line segments depend on a coordinate system of the global unit.h]h/In this example, the east-side ADF will be calculated along the line
segment starting at (10.752,0) and ending at (10.752,10.752). The values
of the line segments depend on a coordinate system of the global unit.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh j1~hhubhM)}(hXFor a reflected model, consider the same type of assembly but
representing an assembly placed on the core periphery. It is bounded on
one side by a 2 cm stainless steel baffle and 10 cm of water, beyond
which is treated as vacuum. Because the reflector calculation is a 1-D
solution, it is not possible to directly model a fuel assembly with two
reflector boundaries. Typically the assumption is made that the same ADF
may be applied in any assembly/reflector boundary and that a 1-D
reflector model is all that is necessary. This model is pictured in
:numref:`fig9-2-43`. Notice that different mixtures are used in the reflector
model. Fluxes used in homogenized mixtures and for generating
homogenized cross sections are spatially averaged; thus, it is important
to separate the moderator in the reflector from that in the fuel
assembly such that average fluxes in each region properly characterize
that region. For example, the flux in the reflector will be
significantly different (far more thermal) from the flux within the
assembly.h](h/X*For a reflected model, consider the same type of assembly but
representing an assembly placed on the core periphery. It is bounded on
one side by a 2 cm stainless steel baffle and 10 cm of water, beyond
which is treated as vacuum. Because the reflector calculation is a 1-D
solution, it is not possible to directly model a fuel assembly with two
reflector boundaries. Typically the assumption is made that the same ADF
may be applied in any assembly/reflector boundary and that a 1-D
reflector model is all that is necessary. This model is pictured in
}(hX*For a reflected model, consider the same type of assembly but
representing an assembly placed on the core periphery. It is bounded on
one side by a 2 cm stainless steel baffle and 10 cm of water, beyond
which is treated as vacuum. Because the reflector calculation is a 1-D
solution, it is not possible to directly model a fuel assembly with two
reflector boundaries. Typically the assumption is made that the same ADF
may be applied in any assembly/reflector boundary and that a 1-D
reflector model is all that is necessary. This model is pictured in
h jhhh!NhNubj)}(h:numref:`fig9-2-43`h]jM)}(hjǁh]h/ fig9-2-43}(hhh jɁubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jŁubah}(h]h]h]h]h]refdochj refdomainjӁreftypenumrefrefexplicitrefwarnjW fig9-2-43uhjh!h"hMh jubh/X. Notice that different mixtures are used in the reflector
model. Fluxes used in homogenized mixtures and for generating
homogenized cross sections are spatially averaged; thus, it is important
to separate the moderator in the reflector from that in the fuel
assembly such that average fluxes in each region properly characterize
that region. For example, the flux in the reflector will be
significantly different (far more thermal) from the flux within the
assembly.}(hX. Notice that different mixtures are used in the reflector
model. Fluxes used in homogenized mixtures and for generating
homogenized cross sections are spatially averaged; thus, it is important
to separate the moderator in the reflector from that in the fuel
assembly such that average fluxes in each region properly characterize
that region. For example, the flux in the reflector will be
significantly different (far more thermal) from the flux within the
assembly.h jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j1~hhubh)}(h.. _fig9-2-43:h]h}(h]h]h]h]h]h fig9-2-43uhh
hMh j1~hhh!h"ubj)}(hhh](j)}(h.. figure:: figs/NEWT/fig43.png
:align: center
:width: 500
Upper-right quadrant of a PWR assembly with baffle and reflector.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig43.pngj*}j,jsuhjh jh!h"hMubj.)}(hAUpper-right quadrant of a PWR assembly with baffle and reflector.h]h/AUpper-right quadrant of a PWR assembly with baffle and reflector.}(hjh j
ubah}(h]h]h]h]h]uhj-h!h"hMh jubeh}(h](id203jeh]h] fig9-2-43ah]h]jEcenteruhjhMh j1~hhh!h"j}j jsj}jjsubhM)}(hXCAssuming again a collapse from 44 energy groups to 2, the following
*collapse*, *homog*, and *adf* blocks would be specified to obtain
2-group ADFs representative of the assembly and the reflector; 2-group
cross sections for each homogenized region would also be prepared from
the collapse and homogenization instructions:h](h/DAssuming again a collapse from 44 energy groups to 2, the following
}(hDAssuming again a collapse from 44 energy groups to 2, the following
h j&hhh!NhNubj)}(h
*collapse*h]h/collapse}(hhh j/ubah}(h]h]h]h]h]uhjh j&ubh/, }(h, h j&hhh!NhNubj)}(h*homog*h]h/homog}(hhh jBubah}(h]h]h]h]h]uhjh j&ubh/, and }(h, and h j&hhh!NhNubj)}(h*adf*h]h/adf}(hhh jUubah}(h]h]h]h]h]uhjh j&ubh/ blocks would be specified to obtain
2-group ADFs representative of the assembly and the reflector; 2-group
cross sections for each homogenized region would also be prepared from
the collapse and homogenization instructions:}(h blocks would be specified to obtain
2-group ADFs representative of the assembly and the reflector; 2-group
cross sections for each homogenized region would also be prepared from
the collapse and homogenization instructions:h j&hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j1~hhubjH)}(hread collapse
22r1 22r2
end collapse
read hmog
500 assm 1 2 3 4 end
501 reflector 5 6 end
end hmog
read adf
2 500 501 w=10.752
end adfh]h/read collapse
22r1 22r2
end collapse
read hmog
500 assm 1 2 3 4 end
501 reflector 5 6 end
end hmog
read adf
2 500 501 w=10.752
end adf}(hhh jnubah}(h]h]h]h]h]j=j>uhjGh!h"hMh j1~hhubh)}(h
.. _9-2-3-12:h]h}(h]h]h]h]h]hid114uhh
hMh j1~hhh!h"ubeh}(h](j%~id113eh]h]9-2-3-11ah]jah]uhh#h jhhh!h"hMBjKj}jj~sj}j%~j~subh$)}(hhh](h))}(hFlux planesh]h/Flux planes}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hMubhM)}(hC**Fluxplane block keyword = fluxplane, fluxplan, flux, fluxplanes**h]h)}(hjh]h/?Fluxplane block keyword = fluxplane, fluxplan, flux, fluxplanes}(hhh jubah}(h]h]h]h]h]uhhh jubah}(h]h]h]h]h]uhhLh!h"hMh jhhubhM)}(hXThe fluxplane block is a special output edit that lets one obtain the
average scalar flux and currents along any line segment or any
continuous set of collinear line segments. One must simply specify the
start and end points of a line segment for which a linearly averaged
flux is desired. This line segment must correspond to one or more line
segments in the model’s grid structure, which requires some knowledge of
where grid lines exist in the model.h]h/XThe fluxplane block is a special output edit that lets one obtain the
average scalar flux and currents along any line segment or any
continuous set of collinear line segments. One must simply specify the
start and end points of a line segment for which a linearly averaged
flux is desired. This line segment must correspond to one or more line
segments in the model’s grid structure, which requires some knowledge of
where grid lines exist in the model.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jhhubhM)}(h7The format of a flux plane specification is as follows:h]h/7The format of a flux plane specification is as follows:}(hjɂh jǂhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM
h jhhubjH)}(hPread fluxplane
text_label homg_assm_id xstart ystart xend yend
…
end fluxplaneh]h/Pread fluxplane
text_label homg_assm_id xstart ystart xend yend
…
end fluxplane}(hhh jՂubah}(h]h]h]h]h]j=j>uhjGh!h"hMh jhhubhM)}(hXwhere *text_label* is an alphanumeric description used to label the
selected plane in the output, *homg_assm_id* is the identifier in the
*homog* block, and *(xstart, y\ start)* and *(xend, y\ end)* are the
start and end points, respectively, for the line segment for which an
average flux is desired. The *text_label* string must not contain white
space and may be up to 16 characters in length.h](h/where }(hwhere h jhhh!NhNubj)}(h*text_label*h]h/
text_label}(hhh jubah}(h]h]h]h]h]uhjh jubh/P is an alphanumeric description used to label the
selected plane in the output, }(hP is an alphanumeric description used to label the
selected plane in the output, h jhhh!NhNubj)}(h*homg_assm_id*h]h/homg_assm_id}(hhh jubah}(h]h]h]h]h]uhjh jubh/ is the identifier in the
}(h is the identifier in the
h jhhh!NhNubj)}(h*homog*h]h/homog}(hhh jubah}(h]h]h]h]h]uhjh jubh/ block, and }(h block, and h jhhh!NhNubj)}(h*(xstart, y\ start)*h]h/(xstart, y start)}(hhh j%ubah}(h]h]h]h]h]uhjh jubh/ and }(h and h jhhh!NhNubj)}(h*(xend, y\ end)*h]h/(xend, y end)}(hhh j8ubah}(h]h]h]h]h]uhjh jubh/l are the
start and end points, respectively, for the line segment for which an
average flux is desired. The }(hl are the
start and end points, respectively, for the line segment for which an
average flux is desired. The h jhhh!NhNubj)}(h*text_label*h]h/
text_label}(hhh jKubah}(h]h]h]h]h]uhjh jubh/N string must not contain white
space and may be up to 16 characters in length.}(hN string must not contain white
space and may be up to 16 characters in length.h jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jhhubhM)}(h]As an example, we consider a simple model consisting of two dissimilar
pin cells (1/4 cells):h]h/]As an example, we consider a simple model consisting of two dissimilar
pin cells (1/4 cells):}(hjfh jdhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jhhubjH)}(hXbglobal unit 1
cuboid 1 1.26 0.0 0.63 0.0
cylinder 2 .4750 chord +x=0 chord +y=0 sides=20
cylinder 3 .4095 chord +x=0 chord +y=0 sides=20
cylinder 4 .6030 chord +y=0 chord -x=1.26 origin x=1.26 sides=20
cylinder 5 .5630 chord +y=0 chord -x=1.26 origin x=1.26 sides=20
media 1 1 3
media 2 1 2 -3
media 10 1 5
media 2 1 4 -5
media 3 1 1 -2 -4
boundary 1 4 2h]h/Xbglobal unit 1
cuboid 1 1.26 0.0 0.63 0.0
cylinder 2 .4750 chord +x=0 chord +y=0 sides=20
cylinder 3 .4095 chord +x=0 chord +y=0 sides=20
cylinder 4 .6030 chord +y=0 chord -x=1.26 origin x=1.26 sides=20
cylinder 5 .5630 chord +y=0 chord -x=1.26 origin x=1.26 sides=20
media 1 1 3
media 2 1 2 -3
media 10 1 5
media 2 1 4 -5
media 3 1 1 -2 -4
boundary 1 4 2}(hhh jrubah}(h]h]h]h]h]j=j>uhjGh!h"hMh jhhubj)}(h=.. image:: figs/NEWT/img1.png
:align: center
:width: 400
h]h}(h]h]h]h]h]aligncenterwidth400urifigs/NEWT/img1.pngj*}j,jsuhjh jhhh!h"hNubhM)}(hWe know a line segment (actually, two) exists at *x* = 0, *x* = 0.63,
and *x* = 1.26, between *y* = 0 and *y* = 0.63. Thus, a legitimate set
of flux plane specifications would be the following:h](h/1We know a line segment (actually, two) exists at }(h1We know a line segment (actually, two) exists at h jhhh!NhNubj)}(h*x*h]h/x}(hhh jubah}(h]h]h]h]h]uhjh jubh/ = 0, }(h = 0, h jhhh!NhNubj)}(h*x*h]h/x}(hhh jubah}(h]h]h]h]h]uhjh jubh/
= 0.63,
and }(h
= 0.63,
and h jhhh!NhNubj)}(h*x*h]h/x}(hhh jubah}(h]h]h]h]h]uhjh jubh/ = 1.26, between }(h = 1.26, between h jhhh!NhNubj)}(h*y*h]h/y}(hhh jӃubah}(h]h]h]h]h]uhjh jubh/ = 0 and }(h = 0 and h jhhh!NhNubj)}(h*y*h]h/y}(hhh jubah}(h]h]h]h]h]uhjh jubh/T = 0.63. Thus, a legitimate set
of flux plane specifications would be the following:}(hT = 0.63. Thus, a legitimate set
of flux plane specifications would be the following:h jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM0h jhhubjH)}(hread fluxplane
cell_interface 0.63 0.0 0.63 0.63
midplane_cell1 0.0 0.0 0.0 0.63
midplane_cell2 1.26 0.0 1.26 0.63
end fluxplaneh]h/read fluxplane
cell_interface 0.63 0.0 0.63 0.63
midplane_cell1 0.0 0.0 0.0 0.63
midplane_cell2 1.26 0.0 1.26 0.63
end fluxplane}(hhh jubah}(h]h]h]h]h]j=j>uhjGh!h"hM6h jhhubhM)}(hThis will provide a summary of fluxes and currents at each line segment in
fine-group structure, and if a collapse is performed, in broad-group structure.
Results from a calculation with a two-group collapse appear as follows:h]h/This will provide a summary of fluxes and currents at each line segment in
fine-group structure, and if a collapse is performed, in broad-group structure.
Results from a calculation with a two-group collapse appear as follows:}(hjh j
hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM=h jhhubjH)}(hXhBroad Group Fluxes:
Group cell_interface midplane_cell1 midplane_cell2
1 5.906586D+01 5.903113D+01 5.930420D+01
2 7.645792D+00 7.641424D+00 6.705809D+00
Broad Group Currents (x):
Group cell_interface midplane_cell1 midplane_cell2
1 -3.481505D-01 0.000000D+00 0.000000D+00
2 3.004759D-01 0.000000D+00 0.000000D+00
Broad Group Currents (y):
Group cell_interface midplane_cell1 midplane_cell2
1 1.081450D-01 1.652161D-01 1.120160D-01
2 -1.031163D-01 -1.647396D-01 -9.993214D-02h]h/XhBroad Group Fluxes:
Group cell_interface midplane_cell1 midplane_cell2
1 5.906586D+01 5.903113D+01 5.930420D+01
2 7.645792D+00 7.641424D+00 6.705809D+00
Broad Group Currents (x):
Group cell_interface midplane_cell1 midplane_cell2
1 -3.481505D-01 0.000000D+00 0.000000D+00
2 3.004759D-01 0.000000D+00 0.000000D+00
Broad Group Currents (y):
Group cell_interface midplane_cell1 midplane_cell2
1 1.081450D-01 1.652161D-01 1.120160D-01
2 -1.031163D-01 -1.647396D-01 -9.993214D-02}(hhh jubah}(h]h]h]h]h]j=j>uhjGh!h"hMDh jhhubhM)}(hCOutput also includes +x, –x, +y, and –y components of currents.h]h/COutput also includes +x, –x, +y, and –y components of currents.}(hj+h j)hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMTh jhhubh)}(h
.. _9-2-3-13:h]h}(h]h]h]h]h]hid115uhh
hMVh jhhh!h"ubeh}(h](flux-planesjeh]h](flux planes9-2-3-12eh]h]uhh#h jhhh!h"hMj}jHj|sj}jj|subh$)}(hhh](h))}(hMixing table blockh]h/Mixing table block}(hjRh jPhhh!NhNubah}(h]h]h]h]h]uhh(h jMhhh!h"hMYubhM)}(h/**Mixing table block keyword = mixt, mixtable**h]h)}(hj`h]h/+Mixing table block keyword = mixt, mixtable}(hhh jbubah}(h]h]h]h]h]uhhh j^ubah}(h]h]h]h]h]uhhLh!h"hM[h jMhhubhM)}(hXGenerally, NEWT calculations are performed using a cross section library
and mixing table prepared in advance by other SCALE modules. However,
NEWT allows the user the ability to manually specify the isotopic
composition of each mixture used in a NEWT model. If a mixing table
block is read, any existing mixing table data file is ignored.
Therefore, all mixtures specified in the material block must be mixed in
the mixing table block.h]h/XGenerally, NEWT calculations are performed using a cross section library
and mixing table prepared in advance by other SCALE modules. However,
NEWT allows the user the ability to manually specify the isotopic
composition of each mixture used in a NEWT model. If a mixing table
block is read, any existing mixing table data file is ignored.
Therefore, all mixtures specified in the material block must be mixed in
the mixing table block.}(hjwh juhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM]h jMhhubhM)}(hXMThe format of the mixing table is simple and straightforward. For each
nuclide used, three parameters must be supplied: (1) *mixid*, the
mixture ID number into which the nuclide is to be mixed;
(2) *nuclideid*, the SCALE ID number for the nuclide (which must exist
on the cross section library being referenced); and (3) *concentration*,
the number density (atoms/b-cm) of the nuclide in this mixture. The same
nuclide may appear in multiple mixtures or more than once in a single
mixture if desired. Macroscopic cross sections are determined for each
mixture by the following formula:h](h/}The format of the mixing table is simple and straightforward. For each
nuclide used, three parameters must be supplied: (1) }(h}The format of the mixing table is simple and straightforward. For each
nuclide used, three parameters must be supplied: (1) h jhhh!NhNubj)}(h*mixid*h]h/mixid}(hhh jubah}(h]h]h]h]h]uhjh jubh/D, the
mixture ID number into which the nuclide is to be mixed;
(2) }(hD, the
mixture ID number into which the nuclide is to be mixed;
(2) h jhhh!NhNubj)}(h*nuclideid*h]h/ nuclideid}(hhh jubah}(h]h]h]h]h]uhjh jubh/q, the SCALE ID number for the nuclide (which must exist
on the cross section library being referenced); and (3) }(hq, the SCALE ID number for the nuclide (which must exist
on the cross section library being referenced); and (3) h jhhh!NhNubj)}(h*concentration*h]h/
concentration}(hhh jubah}(h]h]h]h]h]uhjh jubh/,
the number density (atoms/b-cm) of the nuclide in this mixture. The same
nuclide may appear in multiple mixtures or more than once in a single
mixture if desired. Macroscopic cross sections are determined for each
mixture by the following formula:}(h,
the number density (atoms/b-cm) of the nuclide in this mixture. The same
nuclide may appear in multiple mixtures or more than once in a single
mixture if desired. Macroscopic cross sections are determined for each
mixture by the following formula:h jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMeh jMhhubj))}(h(\Sigma^{R}=\sum_{i} \sigma_{i}^{R} N_{i}h]h/(\Sigma^{R}=\sum_{i} \sigma_{i}^{R} N_{i}}(hhh j˄ubah}(h]h]h]h]h]docnamehjnumberNlabelNnowrapj=j>uhj(h!h"hMoh jMhhubhM)}(hwhereh]h/where}(hj߄h j݄hhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMsh jMhhubjP)}(hhh](hM)}(h[:math:`\Sigma^{R}` is the mixed macroscopic cross section for reaction *R* in the mixture,h](jY)}(h:math:`\Sigma^{R}`h]h/
\Sigma^{R}}(hhh jubah}(h]h]h]h]h]uhjXh jubh/6 is the mixed macroscopic cross section for reaction }(h6 is the mixed macroscopic cross section for reaction h jubj)}(h*R*h]h/R}(hhh jubah}(h]h]h]h]h]uhjh jubh/ in the mixture,}(h in the mixture,h jubeh}(h]h]h]h]h]uhhLh!h"hMuh jubhM)}(h1N\ :sub:`i` is the number density of nuclide *i*,h](h/N }(hN\ h jubj)}(h:sub:`i`h]h/i}(hhh j'ubah}(h]h]h]h]h]uhjh jubh/" is the number density of nuclide }(h" is the number density of nuclide h jubj)}(h*i*h]h/i}(hhh j:ubah}(h]h]h]h]h]uhjh jubh/,}(hjzh jubeh}(h]h]h]h]h]uhhLh!h"hMwh jubhM)}(hY:math:`\sigma_{i}^{R}` is the microscopic cross section for reaction *R* in nuclide *i*.h](jY)}(h:math:`\sigma_{i}^{R}`h]h/\sigma_{i}^{R}}(hhh jVubah}(h]h]h]h]h]uhjXh jRubh/0 is the microscopic cross section for reaction }(h0 is the microscopic cross section for reaction h jRubj)}(h*R*h]h/R}(hhh jiubah}(h]h]h]h]h]uhjh jRubh/ in nuclide }(h in nuclide h jRubj)}(h*i*h]h/i}(hhh j|ubah}(h]h]h]h]h]uhjh jRubh/.}(hhh jRubeh}(h]h]h]h]h]uhhLh!h"hMyh jubeh}(h]h]h]h]h]uhjOh jMhhh!h"hNubhM)}(h1The form of the mixing table block is as follows:h]h/1The form of the mixing table block is as follows:}(hjh jhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM{h jMhhubjH)}(hread mixt
mixid1 nuclideid1 concentration1
mixid2 nuclideid2 concentration2
mixid3 nuclideid3 concentration3
…
mixidN nuclideidN concentrationN
end mixth]h/read mixt
mixid1 nuclideid1 concentration1
mixid2 nuclideid2 concentration2
mixid3 nuclideid3 concentration3
…
mixidN nuclideidN concentrationN
end mixt}(hhh jubah}(h]h]h]h]h]j=j>uhjGh!h"hMh jMhhubhM)}(hX-This concludes this list of input blocks available within NEWT. The
following section provides a list of sample inputs used to represent a
variety of configurations and use of codes. These examples are intended
to provide a broader illustration of the use of NEWT in a range of
potential applications.h]h/X-This concludes this list of input blocks available within NEWT. The
following section provides a list of sample inputs used to represent a
variety of configurations and use of codes. These examples are intended
to provide a broader illustration of the use of NEWT in a range of
potential applications.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jMhhubh)}(h
.. _9-2-4:h]h}(h]h]h]h]h]hid116uhh
hMh jMhhh!h"ubeh}(h](mixing-table-blockjAeh]h](mixing table block9-2-3-13eh]h]uhh#h jhhh!h"hMYj}jՅj7sj}jAj7subeh}(h](
input-formatsjeh]h](
input formats9-2-3eh]h]uhh#h h%hhh!h"hMj}jjsj}jjsubh$)}(hhh](h))}(hExamples of Inputsh]h/Examples of Inputs}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hMubhM)}(hXThis section provides annotated sample input listings for three
different model types, showing the use of a number of different options
and approaches in model development for a variety of applications. These
samples use the TRITON T-XSEC sequence to prepare cross sections for
stand-alone NEWT calculations. In general, this is more easily
accomplished as a TRITON T-NEWT calculation in which cross section
processing and a NEWT transport solution are combined into a single
calculation. However, the user is directed to the TRITON user’s manual
(Chapter `T1.4 `__ of
the SCALE manual) for details on T-XSEC and T‑NEWT calculations. The
examples are intended simply to demonstrate the use of the NEWT code.
The T-XSEC data are included to allow a user to observe the mixture
definitions used in the NEWT input in its calculation. These problems
are also available as sample problems in the SCALE distribution.h](h/X/This section provides annotated sample input listings for three
different model types, showing the use of a number of different options
and approaches in model development for a variety of applications. These
samples use the TRITON T-XSEC sequence to prepare cross sections for
stand-alone NEWT calculations. In general, this is more easily
accomplished as a TRITON T-NEWT calculation in which cross section
processing and a NEWT transport solution are combined into a single
calculation. However, the user is directed to the TRITON user’s manual
(Chapter }(hX/This section provides annotated sample input listings for three
different model types, showing the use of a number of different options
and approaches in model development for a variety of applications. These
samples use the TRITON T-XSEC sequence to prepare cross sections for
stand-alone NEWT calculations. In general, this is more easily
accomplished as a TRITON T-NEWT calculation in which cross section
processing and a NEWT transport solution are combined into a single
calculation. However, the user is directed to the TRITON user’s manual
(Chapter h jhhh!NhNubh reference)}(h9`T1.4 `__h]h/T1.4}(hT1.4h jubah}(h]h]h]h]h]namej refuri)file:///\nstdsrvusersm8jmrrsT01triton.pdfuhjh jubh/X[ of
the SCALE manual) for details on T-XSEC and T‑NEWT calculations. The
examples are intended simply to demonstrate the use of the NEWT code.
The T-XSEC data are included to allow a user to observe the mixture
definitions used in the NEWT input in its calculation. These problems
are also available as sample problems in the SCALE distribution.}(hX[ of
the SCALE manual) for details on T-XSEC and T‑NEWT calculations. The
examples are intended simply to demonstrate the use of the NEWT code.
The T-XSEC data are included to allow a user to observe the mixture
definitions used in the NEWT input in its calculation. These problems
are also available as sample problems in the SCALE distribution.h jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jhhubh)}(h.. _9-2-4-1:h]h}(h]h]h]h]h]hid117uhh
hMh jhhh!h"ubh$)}(hhh](h))}(hSample 1h]h/Sample 1}(hj.h j,hhh!NhNubah}(h]h]h]h]h]uhh(h j)hhh!h"hMubhM)}(hXSample 1 illustrates the use of a series of three consecutive
stand-alone NEWT calculations. Annotated input for this problem is given
in :numref:`fig9-2-44`. The calculation begins with SCALE standard composition
specifications used to prepare a problem-specific weighted cross section
library and mixing table for use by NEWT. In this case the T-XSEC
sequence of the TRITON control module is used. This input is described
in the TRITON chapter and is not described further here.h](h/Sample 1 illustrates the use of a series of three consecutive
stand-alone NEWT calculations. Annotated input for this problem is given
in }(hSample 1 illustrates the use of a series of three consecutive
stand-alone NEWT calculations. Annotated input for this problem is given
in h j:hhh!NhNubj)}(h:numref:`fig9-2-44`h]jM)}(hjEh]h/ fig9-2-44}(hhh jGubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jCubah}(h]h]h]h]h]refdochj refdomainjQreftypenumrefrefexplicitrefwarnjW fig9-2-44uhjh!h"hMh j:ubh/XC. The calculation begins with SCALE standard composition
specifications used to prepare a problem-specific weighted cross section
library and mixing table for use by NEWT. In this case the T-XSEC
sequence of the TRITON control module is used. This input is described
in the TRITON chapter and is not described further here.}(hXC. The calculation begins with SCALE standard composition
specifications used to prepare a problem-specific weighted cross section
library and mixing table for use by NEWT. In this case the T-XSEC
sequence of the TRITON control module is used. This input is described
in the TRITON chapter and is not described further here.h j:hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j)hhubhM)}(hXVThe first NEWT case uses no parameter block; thus, all default
parameters are applied. The default is an eigenvalue calculation, with
cross sections read from ft04f001 (xnlib=4) and collapsed cross sections
written to ft30f001 (wtdlib=30). The 238-group cross section library is
collapsed to a 44‑group library using mixture-weighted fluxes. The model
calculates the eigenvalue for a simple 1/4 pin cell. The center of the
pin is placed at the origin, the lower-left corner of the global unit
boundary, inlaid into a 2 by 2 base grid. The grid structure is
illustrated in :numref:`fig9-2-45`.h](h/XBThe first NEWT case uses no parameter block; thus, all default
parameters are applied. The default is an eigenvalue calculation, with
cross sections read from ft04f001 (xnlib=4) and collapsed cross sections
written to ft30f001 (wtdlib=30). The 238-group cross section library is
collapsed to a 44‑group library using mixture-weighted fluxes. The model
calculates the eigenvalue for a simple 1/4 pin cell. The center of the
pin is placed at the origin, the lower-left corner of the global unit
boundary, inlaid into a 2 by 2 base grid. The grid structure is
illustrated in }(hXBThe first NEWT case uses no parameter block; thus, all default
parameters are applied. The default is an eigenvalue calculation, with
cross sections read from ft04f001 (xnlib=4) and collapsed cross sections
written to ft30f001 (wtdlib=30). The 238-group cross section library is
collapsed to a 44‑group library using mixture-weighted fluxes. The model
calculates the eigenvalue for a simple 1/4 pin cell. The center of the
pin is placed at the origin, the lower-left corner of the global unit
boundary, inlaid into a 2 by 2 base grid. The grid structure is
illustrated in h jnhhh!NhNubj)}(h:numref:`fig9-2-45`h]jM)}(hjyh]h/ fig9-2-45}(hhh j{ubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jwubah}(h]h]h]h]h]refdochj refdomainjreftypenumrefrefexplicitrefwarnjW fig9-2-45uhjh!h"hMh jnubh/.}(hhh jnhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j)hhubhM)}(hXfThe second case performs the same calculation using the collapsed cross
section library created by the first case. Parameter *restart*\ =no is
set to prevent the code from attempting a restart from the existing
library. Because the first case saved 238-group fluxes and the second
case uses 44 energy groups from the collapsed set, a restart is not
possible.h](h/}The second case performs the same calculation using the collapsed cross
section library created by the first case. Parameter }(h}The second case performs the same calculation using the collapsed cross
section library created by the first case. Parameter h jhhh!NhNubj)}(h *restart*h]h/restart}(hhh jubah}(h]h]h]h]h]uhjh jubh/ =no is
set to prevent the code from attempting a restart from the existing
library. Because the first case saved 238-group fluxes and the second
case uses 44 energy groups from the collapsed set, a restart is not
possible.}(h\ =no is
set to prevent the code from attempting a restart from the existing
library. Because the first case saved 238-group fluxes and the second
case uses 44 energy groups from the collapsed set, a restart is not
possible.h jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j)hhubhM)}(hXThe third NEWT case is a calculation identical to the second case,
although the input is different. In this case, the flux restart file
from the previous calculation is used as a first guess for fluxes. This
is permitted since both cases used the same cross section library and
therefore have the same energy boundaries. For this case, the “read
geom” data block is omitted, telling NEWT to use the geometry restart
file from the previous case. This allows a rapid restart, since no
geometric data need to be recomputed. Because no other parameters are
changed, this case will converge after one outer iteration to the same
eigenvalue as in the first case.h]h/XThe third NEWT case is a calculation identical to the second case,
although the input is different. In this case, the flux restart file
from the previous calculation is used as a first guess for fluxes. This
is permitted since both cases used the same cross section library and
therefore have the same energy boundaries. For this case, the “read
geom” data block is omitted, telling NEWT to use the geometry restart
file from the previous case. This allows a rapid restart, since no
geometric data need to be recomputed. Because no other parameters are
changed, this case will converge after one outer iteration to the same
eigenvalue as in the first case.}(hjņh jÆhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh j)hhubh)}(h.. _fig9-2-44:h]h}(h]h]h]h]h]h fig9-2-44uhh
hMh j)hhh!h"ubj)}(hhh](j)}(hg.. figure:: figs/NEWT/fig44.svg
:align: center
:width: 1000
Sample 1 input listing (annotated).
h]h}(h]h]h]h]h]width1000urifigs/NEWT/fig44.svgj*}j,jsuhjh j܆h!h"hMubj.)}(h#Sample 1 input listing (annotated).h]h/#Sample 1 input listing (annotated).}(hjh jubah}(h]h]h]h]h]uhj-h!h"hMh j܆ubeh}(h](id204jۆeh]h] fig9-2-44ah]h]jEcenteruhjhMh j)hhh!h"j}jjцsj}jۆjцsubh)}(h.. _fig9-2-45:h]h}(h]h]h]h]h]h fig9-2-45uhh
hMh j)hhh!h"ubj)}(hhh](j)}(ho.. figure:: figs/NEWT/fig45.png
:align: center
:width: 500
Grid structure for 1/4 pin cell of Sample 1.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig45.pngj*}j,j"suhjh jh!h"hMubj.)}(h,Grid structure for 1/4 pin cell of Sample 1.h]h/,Grid structure for 1/4 pin cell of Sample 1.}(hj&h j$ubah}(h]h]h]h]h]uhj-h!h"hMh jubeh}(h](id205jeh]h] fig9-2-45ah]h]jEcenteruhjhMh j)hhh!h"j}j7jsj}jjsubh)}(h.. _9-2-4-2:h]h}(h]h]h]h]h]hid118uhh
hMh j)hhh!h"ubeh}(h](sample-1j(eh]h](sample 19-2-4-1eh]h]uhh#h jhhh!h"hMj}jNjsj}j(jsubh$)}(hhh](h))}(hSample 2h]h/Sample 2}(hjXh jVhhh!NhNubah}(h]h]h]h]h]uhh(h jShhh!h"hMubhM)}(hXOSample 2 (shown in Figure 9.2.46 and Figure 9.2.47) illustrates the use
of multiple bodies within a single unit. It highlights the use of media
definitions to include and exclude regions when various bodies are used.
Although an array can be used to place bodies, this example illustrates
a method suitable for use in developing a model for a configuration with
an irregular non-array-type structure. This sample problem also
highlights the use of partial-current unstructured-mesh CMFD
acceleration, which reduces the number of outer iterations from 35 to 21
and the CPU run time by ~25%.h]h/XOSample 2 (shown in Figure 9.2.46 and Figure 9.2.47) illustrates the use
of multiple bodies within a single unit. It highlights the use of media
definitions to include and exclude regions when various bodies are used.
Although an array can be used to place bodies, this example illustrates
a method suitable for use in developing a model for a configuration with
an irregular non-array-type structure. This sample problem also
highlights the use of partial-current unstructured-mesh CMFD
acceleration, which reduces the number of outer iterations from 35 to 21
and the CPU run time by ~25%.}(hjfh jdhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jShhubh)}(h.. _fig9-2-46:h]h}(h]h]h]h]h]h fig9-2-46uhh
hMh jShhh!h"ubj)}(hhh](j)}(hg.. figure:: figs/NEWT/fig46.svg
:align: center
:width: 1000
Sample 2 input listing (annotated).
h]h}(h]h]h]h]h]width1000urifigs/NEWT/fig46.svgj*}j,jsuhjh j}h!h"hMubj.)}(h#Sample 2 input listing (annotated).h]h/#Sample 2 input listing (annotated).}(hjh jubah}(h]h]h]h]h]uhj-h!h"hMh j}ubeh}(h](id206j|eh]h] fig9-2-46ah]h]jEcenteruhjhMh jShhh!h"j}jjrsj}j|jrsubh)}(h.. _fig9-2-47:h]h}(h]h]h]h]h]h fig9-2-47uhh
hMh jShhh!h"ubj)}(hhh](j)}(h.. figure:: figs/NEWT/fig47.png
:align: center
:width: 500
Mixture placement and grid structure for model described in Sample 2.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig47.pngj*}j,jÇsuhjh jh!h"hMubj.)}(hEMixture placement and grid structure for model described in Sample 2.h]h/EMixture placement and grid structure for model described in Sample 2.}(hjǇh jŇubah}(h]h]h]h]h]uhj-h!h"hMh jubeh}(h](id207jeh]h] fig9-2-47ah]h]jEcenteruhjhMh jShhh!h"j}j؇jsj}jjsubh)}(h.. _9-2-4-3:h]h}(h]h]h]h]h]hid119uhh
hMh jShhh!h"ubh$)}(hhh](h))}(hSample 3h]h/Sample 3}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hMubhM)}(hSample 3 demonstrates the development of a VVER-440 hexagonal fuel
assembly. Annotated input for this problem is given in Figure 9.2.48.
The output plot for this model is shown in Figure 9.2.49. The key
attributes of this model are as follows:h]h/Sample 3 demonstrates the development of a VVER-440 hexagonal fuel
assembly. Annotated input for this problem is given in Figure 9.2.48.
The output plot for this model is shown in Figure 9.2.49. The key
attributes of this model are as follows:}(hjh jhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jhhubh;)}(hhh](h@)}(hDthe use of hexagonal (hexprism) units in a stacked hexagonal array,
h]hM)}(hCthe use of hexagonal (hexprism) units in a stacked hexagonal array,h]h/Cthe use of hexagonal (hexprism) units in a stacked hexagonal array,}(hjh jubah}(h]h]h]h]h]uhhLh!h"hMh jubah}(h]h]h]h]h]uhh?h jhhh!h"hNubh@)}(h4the use of null units as placeholders in the array,
h]hM)}(h3the use of null units as placeholders in the array,h]h/3the use of null units as placeholders in the array,}(hj)h j'ubah}(h]h]h]h]h]uhhLh!h"hMh j#ubah}(h]h]h]h]h]uhh?h jhhh!h"hNubh@)}(h1a full model within a rhexagonal outer boundary,
h]hM)}(h0a full model within a rhexagonal outer boundary,h]h/0a full model within a rhexagonal outer boundary,}(hjAh j?ubah}(h]h]h]h]h]uhhLh!h"hMh j;ubah}(h]h]h]h]h]uhh?h jhhh!h"hNubh@)}(h&the use of white boundary conditions,
h]hM)}(h%the use of white boundary conditions,h]h/%the use of white boundary conditions,}(hjYh jWubah}(h]h]h]h]h]uhhLh!h"hMh jSubah}(h]h]h]h]h]uhh?h jhhh!h"hNubh@)}(htthe use of the new partial-current-based unstructured CMFD
acceleration for hexagonal-domain configurations, and
h]h definition_list)}(hhh]h definition_list_item)}(hqthe use of the new partial-current-based unstructured CMFD
acceleration for hexagonal-domain configurations, and
h](h term)}(h:the use of the new partial-current-based unstructured CMFDh]h/:the use of the new partial-current-based unstructured CMFD}(hj~h j|ubah}(h]h]h]h]h]uhjzh!h"hMh jvubh
definition)}(hhh]hM)}(h5acceleration for hexagonal-domain configurations, andh]h/5acceleration for hexagonal-domain configurations, and}(hjh jubah}(h]h]h]h]h]uhhLh!h"hMh jubah}(h]h]h]h]h]uhjh jvubeh}(h]h]h]h]h]uhjth!h"hMh jqubah}(h]h]h]h]h]uhjoh jkubah}(h]h]h]h]h]uhh?h jhhh!NhNubh@)}(hnew type-3 ADF inputs.
h]hM)}(hnew type-3 ADF inputs.h]h/new type-3 ADF inputs.}(hjh jubah}(h]h]h]h]h]uhhLh!h"hM
h jubah}(h]h]h]h]h]uhh?h jhhh!h"hNubeh}(h]h]h]h]h]h~j hhhhuhh:h jhhh!h"hMubhM)}(hUsing CMFD acceleration, the number of outer iterations needed for
convergence decreased from 21 to 8 with a run-time speedup of ~2.58.h]h/Using CMFD acceleration, the number of outer iterations needed for
convergence decreased from 21 to 8 with a run-time speedup of ~2.58.}(hjՈh jӈhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jhhubh)}(h.. _fig9-2-48:h]h}(h]h]h]h]h]h fig9-2-48uhh
hMh jhhh!h"ubj)}(hhh](j)}(hv.. figure:: figs/NEWT/fig48.svg
:align: center
:width: 1000
:class: long
Sample 3 input listing (annotated).
h]h}(h]h]longah]h]h]width1000urifigs/NEWT/fig48.svgj*}j,jsuhjh jh!h"hMubj.)}(h#Sample 3 input listing (annotated).h]h/#Sample 3 input listing (annotated).}(hjh jubah}(h]h]h]h]h]uhj-h!h"hMh jubeh}(h](id208jeh]h] fig9-2-48ah]h]jEcenteruhjhMh jhhh!h"j}jjsj}jjsubh)}(h.. _fig9-2-49:h]h}(h]h]h]h]h]h fig9-2-49uhh
hMh jhhh!h"ubj)}(hhh](j)}(h|.. figure:: figs/NEWT/fig49.png
:align: center
:width: 600
Grid structure and material placement for VVER-440 model.
h]h}(h]h]h]h]h]width600urifigs/NEWT/fig49.pngj*}j,j3suhjh j#h!h"hMubj.)}(h9Grid structure and material placement for VVER-440 model.h]h/9Grid structure and material placement for VVER-440 model.}(hj7h j5ubah}(h]h]h]h]h]uhj-h!h"hMh j#ubeh}(h](id209j"eh]h] fig9-2-49ah]h]jEcenteruhjhMh jhhh!h"j}jHjsj}j"jsubh)}(h.. _9-2-4-4:h]h}(h]h]h]h]h]hid120uhh
hMh jhhh!h"ubeh}(h](sample-3jeh]h](sample 39-2-4-3eh]h]uhh#h jShhh!h"hMj}j_jއsj}jjއsubeh}(h](sample-2jGeh]h](sample 29-2-4-2eh]h]uhh#h jhhh!h"hMj}jjj=sj}jGj=subh$)}(hhh](h))}(hSample 4h]h/Sample 4}(hjth jrhhh!NhNubah}(h]h]h]h]h]uhh(h johhh!h"hM!ubhM)}(hXSample 4 demonstrates the use of NEWT in modeling a larger, more complex
configuration. Annotated input for this problem is given in
:numref:`fig9-2-50`. The calculation begins with the use of SCALE standard
composition specifications to prepare a problem-specific weighted cross
section library and mixing table for use by NEWT. In this case the
T-XSEC sequence of the TRITON control module is used.h](h/Sample 4 demonstrates the use of NEWT in modeling a larger, more complex
configuration. Annotated input for this problem is given in
}(hSample 4 demonstrates the use of NEWT in modeling a larger, more complex
configuration. Annotated input for this problem is given in
h jhhh!NhNubj)}(h:numref:`fig9-2-50`h]jM)}(hjh]h/ fig9-2-50}(hhh jubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjreftypenumrefrefexplicitrefwarnjW fig9-2-50uhjh!h"hM#h jubh/. The calculation begins with the use of SCALE standard
composition specifications to prepare a problem-specific weighted cross
section library and mixing table for use by NEWT. In this case the
T-XSEC sequence of the TRITON control module is used.}(h. The calculation begins with the use of SCALE standard
composition specifications to prepare a problem-specific weighted cross
section library and mixing table for use by NEWT. In this case the
T-XSEC sequence of the TRITON control module is used.h jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM#h johhubhM)}(hXdThis NEWT case is used to calculate the eigenvalue of an infinite
lattice of fuel assemblies. Symmetry at the assembly center is used to
reduce a 15 by 15 assembly lattice to a smaller one-quarter assembly.
The grid structure is illustrated in :numref:`fig9-2-51`. A similar
illustration showing media placements by color is given in
:numref:`fig9-2-52`.h](h/This NEWT case is used to calculate the eigenvalue of an infinite
lattice of fuel assemblies. Symmetry at the assembly center is used to
reduce a 15 by 15 assembly lattice to a smaller one-quarter assembly.
The grid structure is illustrated in }(hThis NEWT case is used to calculate the eigenvalue of an infinite
lattice of fuel assemblies. Symmetry at the assembly center is used to
reduce a 15 by 15 assembly lattice to a smaller one-quarter assembly.
The grid structure is illustrated in h jhhh!NhNubj)}(h:numref:`fig9-2-51`h]jM)}(hjh]h/ fig9-2-51}(hhh jubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjˉreftypenumrefrefexplicitrefwarnjW fig9-2-51uhjh!h"hM*h jubh/G. A similar
illustration showing media placements by color is given in
}(hG. A similar
illustration showing media placements by color is given in
h jhhh!NhNubj)}(h:numref:`fig9-2-52`h]jM)}(hjh]h/ fig9-2-52}(hhh jubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjreftypenumrefrefexplicitrefwarnjW fig9-2-52uhjh!h"hM*h jubh/.}(hhh jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM*h johhubhM)}(h|This input illustrates several features of NEWT modeling capabilities.
Some important features of this model are as follows.h]h/|This input illustrates several features of NEWT modeling capabilities.
Some important features of this model are as follows.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hM1h johhubj4)}(hhh](h@)}(hXIn this sample problem, S-6 quadrature, P-1 scattering (P-2 in the
moderator), spatial convergence criteria of 0.005, and an eigenvalue
convergence criteria of 0.001 are used. These are an order of a
magnitude larger than the values typically used for LWR lattice
calculations.
h]hM)}(hXIn this sample problem, S-6 quadrature, P-1 scattering (P-2 in the
moderator), spatial convergence criteria of 0.005, and an eigenvalue
convergence criteria of 0.001 are used. These are an order of a
magnitude larger than the values typically used for LWR lattice
calculations.h]h/XIn this sample problem, S-6 quadrature, P-1 scattering (P-2 in the
moderator), spatial convergence criteria of 0.005, and an eigenvalue
convergence criteria of 0.001 are used. These are an order of a
magnitude larger than the values typically used for LWR lattice
calculations.}(hj#h j!ubah}(h]h]h]h]h]uhhLh!h"hM4h jubah}(h]h]h]h]h]uhh?h jhhh!h"hNubh@)}(hXTwo sets of UO\ :sub:`2` cross sections are prepared in the T-XSEC
calculation. These cross sections are identical with the exception of
the mixture number. Since NEWT reports fluxes, reaction rates, etc.,
by mixture, the placement of a unique mixture at a specific location
in a model allows one to determine, for example, the reaction rates
at that model location. Mixture 7, placed in unit 9 in this model,
occurs in only one pin location in the model. Mixture 1, placed in
all other fuel rod locations, will yield reaction rates close to the
average of those for all fuel in the assembly. If the flux or
reaction rate was needed in each unique fuel location, a unique
mixture would be needed for each location.
h]hM)}(hXTwo sets of UO\ :sub:`2` cross sections are prepared in the T-XSEC
calculation. These cross sections are identical with the exception of
the mixture number. Since NEWT reports fluxes, reaction rates, etc.,
by mixture, the placement of a unique mixture at a specific location
in a model allows one to determine, for example, the reaction rates
at that model location. Mixture 7, placed in unit 9 in this model,
occurs in only one pin location in the model. Mixture 1, placed in
all other fuel rod locations, will yield reaction rates close to the
average of those for all fuel in the assembly. If the flux or
reaction rate was needed in each unique fuel location, a unique
mixture would be needed for each location.h](h/Two sets of UO }(hTwo sets of UO\ h j9ubj)}(h:sub:`2`h]h/2}(hhh jBubah}(h]h]h]h]h]uhjh j9ubh/X cross sections are prepared in the T-XSEC
calculation. These cross sections are identical with the exception of
the mixture number. Since NEWT reports fluxes, reaction rates, etc.,
by mixture, the placement of a unique mixture at a specific location
in a model allows one to determine, for example, the reaction rates
at that model location. Mixture 7, placed in unit 9 in this model,
occurs in only one pin location in the model. Mixture 1, placed in
all other fuel rod locations, will yield reaction rates close to the
average of those for all fuel in the assembly. If the flux or
reaction rate was needed in each unique fuel location, a unique
mixture would be needed for each location.}(hX cross sections are prepared in the T-XSEC
calculation. These cross sections are identical with the exception of
the mixture number. Since NEWT reports fluxes, reaction rates, etc.,
by mixture, the placement of a unique mixture at a specific location
in a model allows one to determine, for example, the reaction rates
at that model location. Mixture 7, placed in unit 9 in this model,
occurs in only one pin location in the model. Mixture 1, placed in
all other fuel rod locations, will yield reaction rates close to the
average of those for all fuel in the assembly. If the flux or
reaction rate was needed in each unique fuel location, a unique
mixture would be needed for each location.h j9ubeh}(h]h]h]h]h]uhhLh!h"hM:h j5ubah}(h]h]h]h]h]uhh?h jhhh!h"hNubh@)}(hXThe use of chords for cutting cylinders allows inclusion of one-half
and one-quarter fuel cells in the quarter-assembly model. Because the
fuel assembly has an odd number of rods in each dimension, use of
symmetry at the assembly midplanes requires the rods to be bisected.
h]hM)}(hXThe use of chords for cutting cylinders allows inclusion of one-half
and one-quarter fuel cells in the quarter-assembly model. Because the
fuel assembly has an odd number of rods in each dimension, use of
symmetry at the assembly midplanes requires the rods to be bisected.h]h/XThe use of chords for cutting cylinders allows inclusion of one-half
and one-quarter fuel cells in the quarter-assembly model. Because the
fuel assembly has an odd number of rods in each dimension, use of
symmetry at the assembly midplanes requires the rods to be bisected.}(hjgh jeubah}(h]h]h]h]h]uhhLh!h"hMFh jaubah}(h]h]h]h]h]uhh?h jhhh!h"hNubh@)}(hX*In this model, local grid spacing was selected such common grid
spacings occur in all cells. However, this is not a requirement. For
example, a much more refined local grid could have been specified for
unit 9. There is no requirement that grid lines match between
different elements of an array.
h]hM)}(hX)In this model, local grid spacing was selected such common grid
spacings occur in all cells. However, this is not a requirement. For
example, a much more refined local grid could have been specified for
unit 9. There is no requirement that grid lines match between
different elements of an array.h]h/X)In this model, local grid spacing was selected such common grid
spacings occur in all cells. However, this is not a requirement. For
example, a much more refined local grid could have been specified for
unit 9. There is no requirement that grid lines match between
different elements of an array.}(hjh j}ubah}(h]h]h]h]h]uhhLh!h"hMKh jyubah}(h]h]h]h]h]uhh?h jhhh!h"hNubh@)}(hXUnstructured coarse-mesh finite-difference acceleration (cmfd=2 or
cmfd=yes) was employed to accelerate the convergence of the solution.
For this case, 14 outer iterations were required for full spatial
convergence as compared with 30 outer iterations when CMFD is
disabled. The CMFD-accelerated case ran 2.5 times faster than its
unaccelerated counterpart. In this sample problem, xycmfd=2 was used
to define the coarse-mesh grid to have two fine-mesh cells per
coarse-mesh cell.
h]hM)}(hXUnstructured coarse-mesh finite-difference acceleration (cmfd=2 or
cmfd=yes) was employed to accelerate the convergence of the solution.
For this case, 14 outer iterations were required for full spatial
convergence as compared with 30 outer iterations when CMFD is
disabled. The CMFD-accelerated case ran 2.5 times faster than its
unaccelerated counterpart. In this sample problem, xycmfd=2 was used
to define the coarse-mesh grid to have two fine-mesh cells per
coarse-mesh cell.h]h/XUnstructured coarse-mesh finite-difference acceleration (cmfd=2 or
cmfd=yes) was employed to accelerate the convergence of the solution.
For this case, 14 outer iterations were required for full spatial
convergence as compared with 30 outer iterations when CMFD is
disabled. The CMFD-accelerated case ran 2.5 times faster than its
unaccelerated counterpart. In this sample problem, xycmfd=2 was used
to define the coarse-mesh grid to have two fine-mesh cells per
coarse-mesh cell.}(hjh jubah}(h]h]h]h]h]uhhLh!h"hMQh jubah}(h]h]h]h]h]uhh?h jhhh!h"hNubh@)}(hXUTwo-group homogenized cross sections were generated along with
single-assembly (i.e., type 1) ADFs derived from the Collapse block,
ADF block, and the Homogenization block. In addition, a B1 critical
spectrum search is computed after the transport calculation, which is
folded into the transport solution to generated homogenized
constants.
h]hM)}(hXTTwo-group homogenized cross sections were generated along with
single-assembly (i.e., type 1) ADFs derived from the Collapse block,
ADF block, and the Homogenization block. In addition, a B1 critical
spectrum search is computed after the transport calculation, which is
folded into the transport solution to generated homogenized
constants.h]h/XTTwo-group homogenized cross sections were generated along with
single-assembly (i.e., type 1) ADFs derived from the Collapse block,
ADF block, and the Homogenization block. In addition, a B1 critical
spectrum search is computed after the transport calculation, which is
folded into the transport solution to generated homogenized
constants.}(hjh jubah}(h]h]h]h]h]uhhLh!h"hMZh jubah}(h]h]h]h]h]uhh?h jhhh!h"hNubeh}(h]h]h]h]h]j4j4uhj4h!h"hM4h johhubh)}(h.. _fig9-2-50:h]h}(h]h]h]h]h]h fig9-2-50uhh
hMah johhh!h"ubj)}(hhh](j)}(hv.. figure:: figs/NEWT/fig50.svg
:align: center
:width: 1000
:class: long
Sample 4 input listing (annotated).
h]h}(h]h]longah]h]h]width1000urifigs/NEWT/fig50.svgj*}j,jsuhjh jҊh!h"hMgubj.)}(h#Sample 4 input listing (annotated).h]h/#Sample 4 input listing (annotated).}(hjh jubah}(h]h]h]h]h]uhj-h!h"hMgh jҊubeh}(h](id210jъeh]h] fig9-2-50ah]h]jEcenteruhjhMgh johhh!h"j}jjǊsj}jъjǊsubh)}(h.. _fig9-2-51:h]h}(h]h]h]h]h]h fig9-2-51uhh
hMih johhh!h"ubj)}(hhh](j)}(hw.. figure:: figs/NEWT/fig51.png
:align: center
:width: 500
Grid structure for one-quarter assembly of Sample 4.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig51.pngj*}j,jsuhjh j h!h"hMnubj.)}(h4Grid structure for one-quarter assembly of Sample 4.h]h/4Grid structure for one-quarter assembly of Sample 4.}(hjh jubah}(h]h]h]h]h]uhj-h!h"hMnh j ubeh}(h](id211jeh]h] fig9-2-51ah]h]jEcenteruhjhMnh johhh!h"j}j.jsj}jjsubh)}(h.. _fig9-2-52:h]h}(h]h]h]h]h]h fig9-2-52uhh
hMph johhh!h"ubj)}(hhh](j)}(h|.. figure:: figs/NEWT/fig52.png
:align: center
:width: 500
Mixture placement for quarter-assembly model of Sample 4.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig52.pngj*}j,jOsuhjh j?h!h"hMuubj.)}(h9Mixture placement for quarter-assembly model of Sample 4.h]h/9Mixture placement for quarter-assembly model of Sample 4.}(hjSh jQubah}(h]h]h]h]h]uhj-h!h"hMuh j?ubeh}(h](id212j>eh]h] fig9-2-52ah]h]jEcenteruhjhMuh johhh!h"j}jdj4sj}j>j4subh)}(h.. _9-2-4-5:h]h}(h]h]h]h]h]hid121uhh
hMwh johhh!h"ubeh}(h](sample-4jXeh]h](sample 49-2-4-4eh]h]uhh#h jhhh!h"hM!j}j{jNsj}jXjNsubh$)}(hhh](h))}(hSample 5h]h/Sample 5}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hMzubhM)}(hX:Sample 5 (:numref:`fig9-2-53`) illustrates a calculation for a fuel assembly
with a large water boundary and a vacuum boundary condition. The
calculation begins with the use of SCALE standard composition
specifications to prepare a problem-specific weighted cross section
library and mixing table for use by NEWT.h](h/Sample 5 (}(hSample 5 (h jhhh!NhNubj)}(h:numref:`fig9-2-53`h]jM)}(hjh]h/ fig9-2-53}(hhh jubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjreftypenumrefrefexplicitrefwarnjW fig9-2-53uhjh!h"hM|h jubh/X) illustrates a calculation for a fuel assembly
with a large water boundary and a vacuum boundary condition. The
calculation begins with the use of SCALE standard composition
specifications to prepare a problem-specific weighted cross section
library and mixing table for use by NEWT.}(hX) illustrates a calculation for a fuel assembly
with a large water boundary and a vacuum boundary condition. The
calculation begins with the use of SCALE standard composition
specifications to prepare a problem-specific weighted cross section
library and mixing table for use by NEWT.h jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM|h jhhubhM)}(hXIn this model, seven UO\ :sub:`2` pins are adjacent to eight MOX pins,
which, in turn, are adjacent to a large reflector region. The outer
boundary of the reflector is vacuum. Reflection on the top and bottom
boundaries makes the problem infinite in the y direction. The grid
structure for this problem is illustrated in :numref:`fig9-2-54`. This problem
illustrates the use of the original CMFD acceleration scheme in NEWT
(cmfd=1 or cmfd=rect). Because of the large degree of scattering within
the reflector region, the problem can be relatively slow to converge.
Without CMFD acceleration, 40 outer iterations are required for spatial
convergence as compared with 12 when CMFD is enabled. A total run-time
speedup of ~1.4 is achieved with the CMFD acceleration scheme.h](h/In this model, seven UO }(hIn this model, seven UO\ h jŋhhh!NhNubj)}(h:sub:`2`h]h/2}(hhh jubah}(h]h]h]h]h]uhjh jŋubh/X! pins are adjacent to eight MOX pins,
which, in turn, are adjacent to a large reflector region. The outer
boundary of the reflector is vacuum. Reflection on the top and bottom
boundaries makes the problem infinite in the y direction. The grid
structure for this problem is illustrated in }(hX! pins are adjacent to eight MOX pins,
which, in turn, are adjacent to a large reflector region. The outer
boundary of the reflector is vacuum. Reflection on the top and bottom
boundaries makes the problem infinite in the y direction. The grid
structure for this problem is illustrated in h jŋhhh!NhNubj)}(h:numref:`fig9-2-54`h]jM)}(hjh]h/ fig9-2-54}(hhh jubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjreftypenumrefrefexplicitrefwarnjW fig9-2-54uhjh!h"hMh jŋubh/X. This problem
illustrates the use of the original CMFD acceleration scheme in NEWT
(cmfd=1 or cmfd=rect). Because of the large degree of scattering within
the reflector region, the problem can be relatively slow to converge.
Without CMFD acceleration, 40 outer iterations are required for spatial
convergence as compared with 12 when CMFD is enabled. A total run-time
speedup of ~1.4 is achieved with the CMFD acceleration scheme.}(hX. This problem
illustrates the use of the original CMFD acceleration scheme in NEWT
(cmfd=1 or cmfd=rect). Because of the large degree of scattering within
the reflector region, the problem can be relatively slow to converge.
Without CMFD acceleration, 40 outer iterations are required for spatial
convergence as compared with 12 when CMFD is enabled. A total run-time
speedup of ~1.4 is achieved with the CMFD acceleration scheme.h jŋhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jhhubhM)}(hIn addition to the application of CMFD, Sample 5 also illustrates the
use of NEWT’s reflector ADF capability. Reflector ADFs are computed
along the fuel/reflector interface.h]h/In addition to the application of CMFD, Sample 5 also illustrates the
use of NEWT’s reflector ADF capability. Reflector ADFs are computed
along the fuel/reflector interface.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jhhubh)}(h.. _fig9-2-53:h]h}(h]h]h]h]h]h fig9-2-53uhh
hMh jhhh!h"ubj)}(hhh](j)}(hv.. figure:: figs/NEWT/fig53.svg
:align: center
:width: 1000
:class: long
Sample 5 input listing (annotated).
h]h}(h]h]longah]h]h]width1000urifigs/NEWT/fig53.svgj*}j,j6suhjh j%h!h"hMubj.)}(h#Sample 5 input listing (annotated).h]h/#Sample 5 input listing (annotated).}(hj:h j8ubah}(h]h]h]h]h]uhj-h!h"hMh j%ubeh}(h](id213j$eh]h] fig9-2-53ah]h]jEcenteruhjhMh jhhh!h"j}jKjsj}j$jsubh)}(h.. _fig9-2-54:h]h}(h]h]h]h]h]h fig9-2-54uhh
hMh jhhh!h"ubj)}(hhh](j)}(hm.. figure:: figs/NEWT/fig54.png
:align: center
:width: 500
Grid structure for 15-pin row of Sample 5.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig54.pngj*}j,jlsuhjh j\h!h"hMubj.)}(h*Grid structure for 15-pin row of Sample 5.h]h/*Grid structure for 15-pin row of Sample 5.}(hjph jnubah}(h]h]h]h]h]uhj-h!h"hMh j\ubeh}(h](id214j[eh]h] fig9-2-54ah]h]jEcenteruhjhMh jhhh!h"j}jjQsj}j[jQsubh)}(h
.. _9-2-5:h]h}(h]h]h]h]h]hid122uhh
hMh jhhh!h"ubh$)}(hhh](h))}(hDescription of Outputh]h/Description of Output}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hMubhM)}(hXThis section contains a brief description and explanation of NEWT
output. Portions of the output will not be printed for every problem.
Some output is optional, depending on user input specifications and is
so noted in the description. As with any SCALE module, output begins
with an input echo, module execution records with times and completion
codes, and the program verification information banner page. These
outputs are common to all SCALE modules and are not described here.h]h/XThis section contains a brief description and explanation of NEWT
output. Portions of the output will not be printed for every problem.
Some output is optional, depending on user input specifications and is
so noted in the description. As with any SCALE module, output begins
with an input echo, module execution records with times and completion
codes, and the program verification information banner page. These
outputs are common to all SCALE modules and are not described here.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jhhubh)}(h.. _9-2-5-1:h]h}(h]h]h]h]h]hid123uhh
hMh jhhh!h"ubeh}(h](description-of-outputjeh]h](description of output9-2-5eh]h]uhh#h jhhh!h"hMj}jjsj}jjsubeh}(h](sample-5jteh]h](sample 59-2-4-5eh]h]uhh#h jhhh!h"hMzj}j͌jjsj}jtjjsubh$)}(hhh](h))}(hNEWT bannerh]h/NEWT banner}(hjh jՌhhh!NhNubah}(h]h]h]h]h]uhh(h jҌhhh!h"hMubhM)}(hX?Following the SCALE program verification information, the first section
unique to NEWT output is the NEWT banner, which appears as shown in
:numref:`fig9-2-55`. The bottom of the banner gives the title of the case as
given in input. The NEWT banner is printed only if the command line
option –p is used to run SCALE.h](h/Following the SCALE program verification information, the first section
unique to NEWT output is the NEWT banner, which appears as shown in
}(hFollowing the SCALE program verification information, the first section
unique to NEWT output is the NEWT banner, which appears as shown in
h jhhh!NhNubj)}(h:numref:`fig9-2-55`h]jM)}(hjh]h/ fig9-2-55}(hhh jubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjreftypenumrefrefexplicitrefwarnjW fig9-2-55uhjh!h"hMh jubh/. The bottom of the banner gives the title of the case as
given in input. The NEWT banner is printed only if the command line
option –p is used to run SCALE.}(h. The bottom of the banner gives the title of the case as
given in input. The NEWT banner is printed only if the command line
option –p is used to run SCALE.h jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jҌhhubh)}(h.. _fig9-2-55:h]h}(h]h]h]h]h]h fig9-2-55uhh
hMh jҌhhh!h"ubj)}(hhh](j)}(hm.. figure:: figs/NEWT/fig55.png
:align: center
:width: 500
NEWT copyright banner page and case title.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig55.pngj*}j,j2suhjh j"h!h"hMubj.)}(h*NEWT copyright banner page and case title.h]h/*NEWT copyright banner page and case title.}(hj6h j4ubah}(h]h]h]h]h]uhj-h!h"hMh j"ubeh}(h](id215j!eh]h] fig9-2-55ah]h]jEcenteruhjhMh jҌhhh!h"j}jGjsj}j!jsubh)}(h.. _9-2-5-2:h]h}(h]h]h]h]h]hid124uhh
hMh jҌhhh!h"ubeh}(h](newt-bannerjeh]h](newt banner9-2-5-1eh]h]uhh#h jhhh!h"hMj}j^jsj}jjsubh$)}(hhh](h))}(h
Input summaryh]h/
Input summary}(hjhh jfhhh!NhNubah}(h]h]h]h]h]uhh(h jchhh!h"hMubhM)}(hXThe next several pages of output provide a summary of input parameters.
As described in :ref:`9-2-5`, default parameters are used when no user
specification is supplied. The input summary lists all parameters and
states used in the calculation, whether user supplied or default. The
following subsections describe the various blocks of output information
provided in the input summary.h](h/XThe next several pages of output provide a summary of input parameters.
As described in }(hXThe next several pages of output provide a summary of input parameters.
As described in h jthhh!NhNubj)}(h:ref:`9-2-5`h]j)}(hjh]h/9-2-5}(hhh jubah}(h]h](jEstdstd-refeh]h]h]uhjh j}ubah}(h]h]h]h]h]refdochj refdomainjreftyperefrefexplicitrefwarnjW9-2-5uhjh!h"hMh jtubh/X, default parameters are used when no user
specification is supplied. The input summary lists all parameters and
states used in the calculation, whether user supplied or default. The
following subsections describe the various blocks of output information
provided in the input summary.}(hX, default parameters are used when no user
specification is supplied. The input summary lists all parameters and
states used in the calculation, whether user supplied or default. The
following subsections describe the various blocks of output information
provided in the input summary.h jthhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jchhubh)}(h.. _9-2-5-2-1:h]h}(h]h]h]h]h]hid125uhh
hMh jchhh!h"ubh$)}(hhh](h))}(hControl optionsh]h/Control options}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hMubhM)}(hX"The Control Options block lists global control parameters that determine
the type of analysis being performed. A sample Control Options page is
shown in :numref:`fig9-2-56`. Parameters are self-explanatory. More
information is available in the description of the keywords in
:ref:`9-2-5-2`.h](h/The Control Options block lists global control parameters that determine
the type of analysis being performed. A sample Control Options page is
shown in }(hThe Control Options block lists global control parameters that determine
the type of analysis being performed. A sample Control Options page is
shown in h jčhhh!NhNubj)}(h:numref:`fig9-2-56`h]jM)}(hjύh]h/ fig9-2-56}(hhh jэubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh j͍ubah}(h]h]h]h]h]refdochj refdomainjۍreftypenumrefrefexplicitrefwarnjW fig9-2-56uhjh!h"hMh jčubh/g. Parameters are self-explanatory. More
information is available in the description of the keywords in
}(hg. Parameters are self-explanatory. More
information is available in the description of the keywords in
h jčhhh!NhNubj)}(h:ref:`9-2-5-2`h]j)}(hjh]h/9-2-5-2}(hhh jubah}(h]h](jEstdstd-refeh]h]h]uhjh jubah}(h]h]h]h]h]refdochj refdomainjreftyperefrefexplicitrefwarnjW9-2-5-2uhjh!h"hMh jčubh/.}(hhh jčhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jhhubh)}(h.. _fig9-2-56:h]h}(h]h]h]h]h]h fig9-2-56uhh
hMh jhhh!h"ubj)}(hhh](j)}(hX.. figure:: figs/NEWT/fig56.svg
:align: center
:width: 600
Control Options page.
h]h}(h]h]h]h]h]width600urifigs/NEWT/fig56.svgj*}j,j7suhjh j'h!h"hMubj.)}(hControl Options page.h]h/Control Options page.}(hj;h j9ubah}(h]h]h]h]h]uhj-h!h"hMh j'ubeh}(h](id216j&eh]h] fig9-2-56ah]h]jEcenteruhjhMh jhhh!h"j}jLjsj}j&jsubh)}(h.. _9-2-5-2-2:h]h}(h]h]h]h]h]hid127uhh
hMh jhhh!h"ubeh}(h](jid126eh]h] 9-2-5-2-1ah]j7ah]uhh#h jchhh!h"hMjKj}jbjsj}jjsubh$)}(hhh](h))}(hOutput optionsh]h/Output options}(hjlh jjhhh!NhNubah}(h]h]h]h]h]uhh(h jghhh!h"hMubhM)}(hThe Output Options block (:numref:`fig9-2-57`) lists selections made for
output. Portions of the output listing will be printed only if the
appropriate printing option was selected.h](h/The Output Options block (}(hThe Output Options block (h jxhhh!NhNubj)}(h:numref:`fig9-2-57`h]jM)}(hjh]h/ fig9-2-57}(hhh jubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjreftypenumrefrefexplicitrefwarnjW fig9-2-57uhjh!h"hMh jxubh/) lists selections made for
output. Portions of the output listing will be printed only if the
appropriate printing option was selected.}(h) lists selections made for
output. Portions of the output listing will be printed only if the
appropriate printing option was selected.h jxhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jghhubh)}(h.. _fig9-2-57:h]h}(h]h]h]h]h]h fig9-2-57uhh
hMh jghhh!h"ubj)}(hhh](j)}(hW.. figure:: figs/NEWT/fig57.svg
:align: center
:width: 600
Output Options page.
h]h}(h]h]h]h]h]width600urifigs/NEWT/fig57.svgj*}j,jǎsuhjh jh!h"hMubj.)}(hOutput Options page.h]h/Output Options page.}(hjˎh jɎubah}(h]h]h]h]h]uhj-h!h"hMh jubeh}(h](id217jeh]h] fig9-2-57ah]h]jEcenteruhjhMh jghhh!h"j}jjsj}jjsubh)}(h.. _9-2-5-2-3:h]h}(h]h]h]h]h]hid128uhh
hMh jghhh!h"ubeh}(h](output-optionsj\eh]h](output options 9-2-5-2-2eh]h]uhh#h jchhh!h"hMj}jjRsj}j\jRsubh$)}(hhh](h))}(hInput/output unit assignmentsh]h/Input/output unit assignments}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hMubhM)}(hThe Input/Output (I/O) Unit Assignments block (:numref:`fig9-2-58`) simply
lists the unit numbers selected for reading or writing various data
files, as appropriate for the calculation.h](h//The Input/Output (I/O) Unit Assignments block (}(h/The Input/Output (I/O) Unit Assignments block (h j hhh!NhNubj)}(h:numref:`fig9-2-58`h]jM)}(hjh]h/ fig9-2-58}(hhh jubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainj reftypenumrefrefexplicitrefwarnjW fig9-2-58uhjh!h"hMh j ubh/w) simply
lists the unit numbers selected for reading or writing various data
files, as appropriate for the calculation.}(hw) simply
lists the unit numbers selected for reading or writing various data
files, as appropriate for the calculation.h j hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jhhubh)}(h.. _fig9-2-58:h]h}(h]h]h]h]h]h fig9-2-58uhh
hMh jhhh!h"ubj)}(hhh](j)}(hf.. figure:: figs/NEWT/fig58.svg
:align: center
:width: 600
Input/Output Unit Assignments page.
h]h}(h]h]h]h]h]width600urifigs/NEWT/fig58.svgj*}j,jXsuhjh jHh!h"hMubj.)}(h#Input/Output Unit Assignments page.h]h/#Input/Output Unit Assignments page.}(hj\h jZubah}(h]h]h]h]h]uhj-h!h"hMh jHubeh}(h](id218jGeh]h] fig9-2-58ah]h]jEcenteruhjhMh jhhh!h"j}jmj=sj}jGj=subh)}(h.. _9-2-5-2-4:h]h}(h]h]h]h]h]hid129uhh
hMh jhhh!h"ubeh}(h](input-output-unit-assignmentsjeh]h](input/output unit assignments 9-2-5-2-3eh]h]uhh#h jchhh!h"hMj}jjsj}jjsubh$)}(hhh](h))}(hConvergence control parametersh]h/Convergence control parameters}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hMubhM)}(hThe Convergence Control block (:numref:`fig9-2-59`) summarizes all parameters
used to control spatial, angular, and eigenvalue convergence for the
iterative phases of the solution process.h](h/The Convergence Control block (}(hThe Convergence Control block (h jhhh!NhNubj)}(h:numref:`fig9-2-59`h]jM)}(hjh]h/ fig9-2-59}(hhh jubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjreftypenumrefrefexplicitrefwarnjW fig9-2-59uhjh!h"hMh jubh/) summarizes all parameters
used to control spatial, angular, and eigenvalue convergence for the
iterative phases of the solution process.}(h) summarizes all parameters
used to control spatial, angular, and eigenvalue convergence for the
iterative phases of the solution process.h jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jhhubh)}(h.. _fig9-2-59:h]h}(h]h]h]h]h]h fig9-2-59uhh
hMh jhhh!h"ubj)}(hhh](j)}(hg.. figure:: figs/NEWT/fig59.svg
:align: center
:width: 600
Convergence Control Parameters page.
h]h}(h]h]h]h]h]width600urifigs/NEWT/fig59.svgj*}j,jsuhjh jُh!h"hMubj.)}(h$Convergence Control Parameters page.h]h/$Convergence Control Parameters page.}(hjh jubah}(h]h]h]h]h]uhj-h!h"hMh jُubeh}(h](id219j؏eh]h] fig9-2-59ah]h]jEcenteruhjhMh jhhh!h"j}jjΏsj}j؏jΏsubh)}(h.. _9-2-5-2-5:h]h}(h]h]h]h]h]hid130uhh
hMh jhhh!h"ubeh}(h](convergence-control-parametersj}eh]h](convergence control parameters 9-2-5-2-4eh]h]uhh#h jchhh!h"hMj}jjssj}j}jssubh$)}(hhh](h))}(hPin-power edit requestsh]h/Pin-power edit requests}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hMubhM)}(hIf pin-power edits are requested for one or more arrays, a listing is
provided of the arrays for which this request was made (:numref:`fig9-2-60`).h](h/~If pin-power edits are requested for one or more arrays, a listing is
provided of the arrays for which this request was made (}(h~If pin-power edits are requested for one or more arrays, a listing is
provided of the arrays for which this request was made (h j+hhh!NhNubj)}(h:numref:`fig9-2-60`h]jM)}(hj6h]h/ fig9-2-60}(hhh j8ubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh j4ubah}(h]h]h]h]h]refdochj refdomainjBreftypenumrefrefexplicitrefwarnjW fig9-2-60uhjh!h"hMh j+ubh/).}(h).h j+hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jhhubh)}(h.. _fig9-2-60:h]h}(h]h]h]h]h]h fig9-2-60uhh
hMh jhhh!h"ubj)}(hhh](j)}(hb.. figure:: figs/NEWT/fig60.svg
:align: center
:width: 600
Pin-power edit request summary.
h]h}(h]h]h]h]h]width600urifigs/NEWT/fig60.svgj*}j,jzsuhjh jjh!h"hMubj.)}(hPin-power edit request summary.h]h/Pin-power edit request summary.}(hj~h j|ubah}(h]h]h]h]h]uhj-h!h"hMh jjubeh}(h](id220jieh]h] fig9-2-60ah]h]jEcenteruhjhMh jhhh!h"j}jj_sj}jij_subh)}(h.. _9-2-5-2-6:h]h}(h]h]h]h]h]hid131uhh
hMh jhhh!h"ubeh}(h](pin-power-edit-requestsjeh]h](pin-power edit requests 9-2-5-2-5eh]h]uhh#h jchhh!h"hMj}jjsj}jjsubh$)}(hhh](h))}(hGeometry specificationsh]h/Geometry specifications}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hM ubhM)}(hXThe Geometry Specifications block (:numref:`fig9-2-61`) lists parameters
associated with the geometric model specified by the user. The first
section lists the characteristics of the global unit. This is followed
by a listing of the four boundary conditions. Finally, the last section
in this block lists all bodies specified for the model. The appearance
and contents of this section of input depend on the nature of the input
model.h](h/#The Geometry Specifications block (}(h#The Geometry Specifications block (h jhhh!NhNubj)}(h:numref:`fig9-2-61`h]jM)}(hjǐh]h/ fig9-2-61}(hhh jɐubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jŐubah}(h]h]h]h]h]refdochj refdomainjӐreftypenumrefrefexplicitrefwarnjW fig9-2-61uhjh!h"hM"h jubh/X|) lists parameters
associated with the geometric model specified by the user. The first
section lists the characteristics of the global unit. This is followed
by a listing of the four boundary conditions. Finally, the last section
in this block lists all bodies specified for the model. The appearance
and contents of this section of input depend on the nature of the input
model.}(hX|) lists parameters
associated with the geometric model specified by the user. The first
section lists the characteristics of the global unit. This is followed
by a listing of the four boundary conditions. Finally, the last section
in this block lists all bodies specified for the model. The appearance
and contents of this section of input depend on the nature of the input
model.h jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM"h jhhubh)}(h.. _fig9-2-61:h]h}(h]h]h]h]h]h fig9-2-61uhh
hM*h jhhh!h"ubj)}(hhh](j)}(h`.. figure:: figs/NEWT/fig61.svg
:align: center
:width: 600
Geometry Specifications page.
h]h}(h]h]h]h]h]width600urifigs/NEWT/fig61.svgj*}j,jsuhjh jh!h"hM/ubj.)}(hGeometry Specifications page.h]h/Geometry Specifications page.}(hjh j
ubah}(h]h]h]h]h]uhj-h!h"hM/h jubeh}(h](id221jeh]h] fig9-2-61ah]h]jEcenteruhjhM/h jhhh!h"j}j jsj}jjsubh)}(h.. _9-2-5-2-7:h]h}(h]h]h]h]h]hid132uhh
hM1h jhhh!h"ubeh}(h](geometry-specificationsjeh]h](geometry specifications 9-2-5-2-6eh]h]uhh#h jchhh!h"hM j}j7jsj}jjsubh$)}(hhh](h))}(h$Homogenization region specificationsh]h/$Homogenization region specifications}(hjAh j?hhh!NhNubah}(h]h]h]h]h]uhh(h j<hhh!h"hM4ubhM)}(hThe Homogenization Region Specifications block (:numref:`fig9-2-62`)
summarizes all sets of homogenized cross sections requested in user
input.h](h/0The Homogenization Region Specifications block (}(h0The Homogenization Region Specifications block (h jMhhh!NhNubj)}(h:numref:`fig9-2-62`h]jM)}(hjXh]h/ fig9-2-62}(hhh jZubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jVubah}(h]h]h]h]h]refdochj refdomainjdreftypenumrefrefexplicitrefwarnjW fig9-2-62uhjh!h"hM6h jMubh/M)
summarizes all sets of homogenized cross sections requested in user
input.}(hM)
summarizes all sets of homogenized cross sections requested in user
input.h jMhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM6h j<hhubh)}(h.. _fig9-2-62:h]h}(h]h]h]h]h]h fig9-2-62uhh
hM:h j<hhh!h"ubj)}(hhh](j)}(hm.. figure:: figs/NEWT/fig62.svg
:align: center
:width: 600
Homogenization Region Specifications page.
h]h}(h]h]h]h]h]width600urifigs/NEWT/fig62.svgj*}j,jsuhjh jh!h"hM?ubj.)}(h*Homogenization Region Specifications page.h]h/*Homogenization Region Specifications page.}(hjh jubah}(h]h]h]h]h]uhj-h!h"hM?h jubeh}(h](id222jeh]h] fig9-2-62ah]h]jEcenteruhjhM?h j<hhh!h"j}jjsj}jjsubh)}(h.. _9-2-5-2-8:h]h}(h]h]h]h]h]hid133uhh
hMAh j<hhh!h"ubeh}(h]($homogenization-region-specificationsj0eh]h]($homogenization region specifications 9-2-5-2-7eh]h]uhh#h jchhh!h"hM4j}jȑj&sj}j0j&subh$)}(hhh](h))}(hMaterial specificationsh]h/Material specifications}(hjґh jБhhh!NhNubah}(h]h]h]h]h]uhh(h j͑hhh!h"hMDubhM)}(hThe Material Specification block (:numref:`fig9-2-63`) lists the NEWT material
number, counting in the order read in; the SCALE mixture number; and the
P\ :sub:`n` order assigned for that mixture.h](h/"The Material Specification block (}(h"The Material Specification block (h jޑhhh!NhNubj)}(h:numref:`fig9-2-63`h]jM)}(hjh]h/ fig9-2-63}(hhh jubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjreftypenumrefrefexplicitrefwarnjW fig9-2-63uhjh!h"hMFh jޑubh/f) lists the NEWT material
number, counting in the order read in; the SCALE mixture number; and the
P }(hf) lists the NEWT material
number, counting in the order read in; the SCALE mixture number; and the
P\ h jޑhhh!NhNubj)}(h:sub:`n`h]h/n}(hhh jubah}(h]h]h]h]h]uhjh jޑubh/! order assigned for that mixture.}(h! order assigned for that mixture.h jޑhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMFh j͑hhubh)}(h.. _fig9-2-63:h]h}(h]h]h]h]h]h fig9-2-63uhh
hMJh j͑hhh!h"ubj)}(hhh](j)}(h`.. figure:: figs/NEWT/fig63.svg
:align: center
:width: 600
Material Specifications page.
h]h}(h]h]h]h]h]width600urifigs/NEWT/fig63.svgj*}j,j@suhjh j0h!h"hMOubj.)}(hMaterial Specifications page.h]h/Material Specifications page.}(hjDh jBubah}(h]h]h]h]h]uhj-h!h"hMOh j0ubeh}(h](id223j/eh]h] fig9-2-63ah]h]jEcenteruhjhMOh j͑hhh!h"j}jUj%sj}j/j%subh)}(h.. _9-2-5-2-9:h]h}(h]h]h]h]h]hid134uhh
hMQh j͑hhh!h"ubeh}(h](material-specificationsjeh]h](material specifications 9-2-5-2-8eh]h]uhh#h jchhh!h"hMDj}jljsj}jjsubh$)}(hhh](h))}(hDerived parametersh]h/Derived parameters}(hjvh jthhh!NhNubah}(h]h]h]h]h]uhh(h jqhhh!h"hMTubhM)}(hXThe Derived Parameters block (:numref:`fig9-2-64`) lists values not
specifically input but derived from other sources of input. Some of this
information comes from the cross section library, some from the model
geometry, and some from the S\ :sub:`n` and P\ :sub:`n` values
specified.h](h/The Derived Parameters block (}(hThe Derived Parameters block (h jhhh!NhNubj)}(h:numref:`fig9-2-64`h]jM)}(hjh]h/ fig9-2-64}(hhh jubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjreftypenumrefrefexplicitrefwarnjW fig9-2-64uhjh!h"hMVh jubh/) lists values not
specifically input but derived from other sources of input. Some of this
information comes from the cross section library, some from the model
geometry, and some from the S }(h) lists values not
specifically input but derived from other sources of input. Some of this
information comes from the cross section library, some from the model
geometry, and some from the S\ h jhhh!NhNubj)}(h:sub:`n`h]h/n}(hhh jubah}(h]h]h]h]h]uhjh jubh/ and P }(h and P\ h jhhh!NhNubj)}(h:sub:`n`h]h/n}(hhh jÒubah}(h]h]h]h]h]uhjh jubh/ values
specified.}(h values
specified.h jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMVh jqhhubh)}(h.. _fig9-2-64:h]h}(h]h]h]h]h]h fig9-2-64uhh
hM\h jqhhh!h"ubj)}(hhh](j)}(h[.. figure:: figs/NEWT/fig64.svg
:align: center
:width: 600
Derived Parameters page.
h]h}(h]h]h]h]h]width600urifigs/NEWT/fig64.svgj*}j,jsuhjh jh!h"hMaubj.)}(hDerived Parameters page.h]h/Derived Parameters page.}(hjh jubah}(h]h]h]h]h]uhj-h!h"hMah jubeh}(h](id224jeh]h] fig9-2-64ah]h]jEcenteruhjhMah jqhhh!h"j}jjܒsj}jjܒsubh)}(h.. _9-2-5-2-10:h]h}(h]h]h]h]h]hid135uhh
hMch jqhhh!h"ubeh}(h](derived-parametersjeeh]h](derived parameters 9-2-5-2-9eh]h]uhh#h jchhh!h"hMTj}j#j[sj}jej[subh$)}(hhh](h))}(hEnergy group structure listingh]h/Energy group structure listing}(hj-h j+hhh!NhNubah}(h]h]h]h]h]uhh(h j(hhh!h"hMfubhM)}(hXThe Energy Group Structures block (:numref:`fig9-2-65`) lists the energy and
lethargy boundaries found in the cross section library. If a broad-group
collapse was requested, the boundaries of the broad-group library that
will be produced are also identified. This example shows the structure
of the SCALE 44GROUPNDF5 library and 2-group fast/thermal collapse
structure. The final entry (group 45, broad group 3) indicates the lower
bound of the previous energy group.h](h/#The Energy Group Structures block (}(h#The Energy Group Structures block (h j9hhh!NhNubj)}(h:numref:`fig9-2-65`h]jM)}(hjDh]h/ fig9-2-65}(hhh jFubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jBubah}(h]h]h]h]h]refdochj refdomainjPreftypenumrefrefexplicitrefwarnjW fig9-2-65uhjh!h"hMhh j9ubh/X) lists the energy and
lethargy boundaries found in the cross section library. If a broad-group
collapse was requested, the boundaries of the broad-group library that
will be produced are also identified. This example shows the structure
of the SCALE 44GROUPNDF5 library and 2-group fast/thermal collapse
structure. The final entry (group 45, broad group 3) indicates the lower
bound of the previous energy group.}(hX) lists the energy and
lethargy boundaries found in the cross section library. If a broad-group
collapse was requested, the boundaries of the broad-group library that
will be produced are also identified. This example shows the structure
of the SCALE 44GROUPNDF5 library and 2-group fast/thermal collapse
structure. The final entry (group 45, broad group 3) indicates the lower
bound of the previous energy group.h j9hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMhh j(hhubh)}(h.. _fig9-2-65:h]h}(h]h]h]h]h]h fig9-2-65uhh
hMph j(hhh!h"ubj)}(hhh](j)}(hg.. figure:: figs/NEWT/fig65.svg
:align: center
:width: 600
Energy Group Structure Listing page.
h]h}(h]h]h]h]h]width600urifigs/NEWT/fig65.svgj*}j,jsuhjh jxh!h"hMuubj.)}(h$Energy Group Structure Listing page.h]h/$Energy Group Structure Listing page.}(hjh jubah}(h]h]h]h]h]uhj-h!h"hMuh jxubeh}(h](id225jweh]h] fig9-2-65ah]h]jEcenteruhjhMuh j(hhh!h"j}jjmsj}jwjmsubh)}(h.. _9-2-5-2-11:h]h}(h]h]h]h]h]hid136uhh
hMwh j(hhh!h"ubeh}(h](energy-group-structure-listingjeh]h](energy group structure listing
9-2-5-2-10eh]h]uhh#h jchhh!h"hMfj}jjsj}jjsubh$)}(hhh](h))}(hQuadrature parametersh]h/Quadrature parameters}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hMzubhM)}(hXThe Quadrature Parameters block (:numref:`fig9-2-66`) lists the first-quadrant
angles and weights used for the specified order of quadrature. The same
angles and weights are applied in the other three quadrants; however,
the signs of the angles vary with the quadrant. Also listed are the
P\ :sub:`n` moments associated with the maximum P\ :sub:`n` scattering
order requested in all materials. Of course, only a subset of these
moments applies to the lower-order P\ :sub:`n` assignments.h](h/!The Quadrature Parameters block (}(h!The Quadrature Parameters block (h jʓhhh!NhNubj)}(h:numref:`fig9-2-66`h]jM)}(hjՓh]h/ fig9-2-66}(hhh jדubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jӓubah}(h]h]h]h]h]refdochj refdomainjreftypenumrefrefexplicitrefwarnjW fig9-2-66uhjh!h"hM|h jʓubh/) lists the first-quadrant
angles and weights used for the specified order of quadrature. The same
angles and weights are applied in the other three quadrants; however,
the signs of the angles vary with the quadrant. Also listed are the
P }(h) lists the first-quadrant
angles and weights used for the specified order of quadrature. The same
angles and weights are applied in the other three quadrants; however,
the signs of the angles vary with the quadrant. Also listed are the
P\ h jʓhhh!NhNubj)}(h:sub:`n`h]h/n}(hhh jubah}(h]h]h]h]h]uhjh jʓubh/) moments associated with the maximum P }(h) moments associated with the maximum P\ h jʓhhh!NhNubj)}(h:sub:`n`h]h/n}(hhh jubah}(h]h]h]h]h]uhjh jʓubh/w scattering
order requested in all materials. Of course, only a subset of these
moments applies to the lower-order P }(hw scattering
order requested in all materials. Of course, only a subset of these
moments applies to the lower-order P\ h jʓhhh!NhNubj)}(h:sub:`n`h]h/n}(hhh jubah}(h]h]h]h]h]uhjh jʓubh/ assignments.}(h assignments.h jʓhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM|h jhhubh)}(h.. _fig9-2-66:h]h}(h]h]h]h]h]h fig9-2-66uhh
hMh jhhh!h"ubj)}(hhh](j)}(h^.. figure:: figs/NEWT/fig66.svg
:align: center
:width: 600
Quadrature Parameters page.
h]h}(h]h]h]h]h]width600urifigs/NEWT/fig66.svgj*}j,jRsuhjh jBh!h"hMubj.)}(hQuadrature Parameters page.h]h/Quadrature Parameters page.}(hjVh jTubah}(h]h]h]h]h]uhj-h!h"hMh jBubeh}(h](id226jAeh]h] fig9-2-66ah]h]jEcenteruhjhMh jhhh!h"j}jgj7sj}jAj7subh)}(h.. _9-2-5-2-12:h]h}(h]h]h]h]h]hid137uhh
hMh jhhh!h"ubeh}(h](quadrature-parametersjeh]h](quadrature parameters
9-2-5-2-11eh]h]uhh#h jchhh!h"hMzj}j~jsj}jjsubh$)}(hhh](h))}(hMixture volumes listingh]h/Mixture volumes listing}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hMubhM)}(hX]The Mixture Volumes block (:numref:`fig9-2-67`) provides a summary of the
volume and volume fraction of each mixture in the problem, together with
the total volume. This block can be used as a simple check of the input
model by ensuring that the calculated volumes of mixtures used for a
given problem match the expected volumes or volume fractions.h](h/The Mixture Volumes block (}(hThe Mixture Volumes block (h jhhh!NhNubj)}(h:numref:`fig9-2-67`h]jM)}(hjh]h/ fig9-2-67}(hhh jubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjreftypenumrefrefexplicitrefwarnjW fig9-2-67uhjh!h"hMh jubh/X/) provides a summary of the
volume and volume fraction of each mixture in the problem, together with
the total volume. This block can be used as a simple check of the input
model by ensuring that the calculated volumes of mixtures used for a
given problem match the expected volumes or volume fractions.}(hX/) provides a summary of the
volume and volume fraction of each mixture in the problem, together with
the total volume. This block can be used as a simple check of the input
model by ensuring that the calculated volumes of mixtures used for a
given problem match the expected volumes or volume fractions.h jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jhhubh)}(h.. _fig9-2-67:h]h}(h]h]h]h]h]h fig9-2-67uhh
hMh jhhh!h"ubj)}(hhh](j)}(hX.. figure:: figs/NEWT/fig67.svg
:align: center
:width: 500
Mixture Volumes page.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig67.svgj*}j,jsuhjh jӔh!h"hMubj.)}(hMixture Volumes page.h]h/Mixture Volumes page.}(hjh jubah}(h]h]h]h]h]uhj-h!h"hMh jӔubeh}(h](id227jҔeh]h] fig9-2-67ah]h]jEcenteruhjhMh jhhh!h"j}jjȔsj}jҔjȔsubh)}(h.. _9-2-5-2-13:h]h}(h]h]h]h]h]hid138uhh
hMh jhhh!h"ubeh}(h](mixture-volumes-listingjweh]h](mixture volumes listing
9-2-5-2-12eh]h]uhh#h jchhh!h"hMj}jjmsj}jwjmsubh$)}(hhh](h))}(hMixing table listingh]h/Mixing table listing}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hMubhM)}(hX}The Mixing Table block summarizes the input mixing table, whether user
supplied or read from a SCALE-generated file. Number densities are in
units of atoms per barn-centimeter. Although optional, the mixing table
is printed by default. This default setting can be disabled by
specifying *prtmxtab*\ =no in the Parameter block. A sample mixing table
is shown in :numref:`fig9-2-68`.h](h/XThe Mixing Table block summarizes the input mixing table, whether user
supplied or read from a SCALE-generated file. Number densities are in
units of atoms per barn-centimeter. Although optional, the mixing table
is printed by default. This default setting can be disabled by
specifying }(hXThe Mixing Table block summarizes the input mixing table, whether user
supplied or read from a SCALE-generated file. Number densities are in
units of atoms per barn-centimeter. Although optional, the mixing table
is printed by default. This default setting can be disabled by
specifying h j%hhh!NhNubj)}(h
*prtmxtab*h]h/prtmxtab}(hhh j.ubah}(h]h]h]h]h]uhjh j%ubh/@ =no in the Parameter block. A sample mixing table
is shown in }(h@\ =no in the Parameter block. A sample mixing table
is shown in h j%hhh!NhNubj)}(h:numref:`fig9-2-68`h]jM)}(hjCh]h/ fig9-2-68}(hhh jEubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jAubah}(h]h]h]h]h]refdochj refdomainjOreftypenumrefrefexplicitrefwarnjW fig9-2-68uhjh!h"hMh j%ubh/.}(hhh j%hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jhhubh)}(h.. _fig9-2-68:h]h}(h]h]h]h]h]h fig9-2-68uhh
hMh jhhh!h"ubj)}(hhh](j)}(h].. figure:: figs/NEWT/fig68.svg
:align: center
:width: 500
Mixing Table Listing page.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig68.svgj*}j,jsuhjh jvh!h"hMubj.)}(hMixing Table Listing page.h]h/Mixing Table Listing page.}(hjh jubah}(h]h]h]h]h]uhj-h!h"hMh jvubeh}(h](id228jueh]h] fig9-2-68ah]h]jEcenteruhjhMh jhhh!h"j}jjksj}jujksubh)}(h.. _9-2-5-2-14:h]h}(h]h]h]h]h]hid139uhh
hMh jhhh!h"ubeh}(h](mixing-table-listingjeh]h](mixing table listing
9-2-5-2-13eh]h]uhh#h jchhh!h"hMj}jjsj}jjsubh$)}(hhh](h))}(hNuclide cross sectionsh]h/Nuclide cross sections}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hMubhM)}(hXThe Nuclide Cross Section block is optional and is printed only when
*prtxsec*\ =yes is specified in the Parameter Block. The volume of
output generated is quite extensive, especially when a very fine group
library is used and/or a large number of nuclides are included in the
mixing table. The nuclide data are taken directly from the working
library used for the calculation. A sample showing a partial listing for
a single nuclide is shown in :numref:`fig9-2-69`.h](h/EThe Nuclide Cross Section block is optional and is printed only when
}(hEThe Nuclide Cross Section block is optional and is printed only when
h jȕhhh!NhNubj)}(h *prtxsec*h]h/prtxsec}(hhh jѕubah}(h]h]h]h]h]uhjh jȕubh/Xp =yes is specified in the Parameter Block. The volume of
output generated is quite extensive, especially when a very fine group
library is used and/or a large number of nuclides are included in the
mixing table. The nuclide data are taken directly from the working
library used for the calculation. A sample showing a partial listing for
a single nuclide is shown in }(hXp\ =yes is specified in the Parameter Block. The volume of
output generated is quite extensive, especially when a very fine group
library is used and/or a large number of nuclides are included in the
mixing table. The nuclide data are taken directly from the working
library used for the calculation. A sample showing a partial listing for
a single nuclide is shown in h jȕhhh!NhNubj)}(h:numref:`fig9-2-69`h]jM)}(hjh]h/ fig9-2-69}(hhh jubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjreftypenumrefrefexplicitrefwarnjW fig9-2-69uhjh!h"hMh jȕubh/.}(hhh jȕhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jhhubhM)}(hXJFollowing the block header, nuclide data are listed for all nuclides.
For each record, the same format is used. Nuclide data begin with a
listing of nuclide header information. This is followed by a listing of
the 1-D cross sections that are important in NEWT calculations. The
sample below shows a partial listing of the 1-D cross sections.
Following the 1-D cross section listing is the scattering matrix for the
nuclide. This abbreviated listing shows a portion of the
P\ :sub:`0` matrix for this nuclide; however, in a full listing, all
higher-order elements are printed as well.h](h/XFollowing the block header, nuclide data are listed for all nuclides.
For each record, the same format is used. Nuclide data begin with a
listing of nuclide header information. This is followed by a listing of
the 1-D cross sections that are important in NEWT calculations. The
sample below shows a partial listing of the 1-D cross sections.
Following the 1-D cross section listing is the scattering matrix for the
nuclide. This abbreviated listing shows a portion of the
P }(hXFollowing the block header, nuclide data are listed for all nuclides.
For each record, the same format is used. Nuclide data begin with a
listing of nuclide header information. This is followed by a listing of
the 1-D cross sections that are important in NEWT calculations. The
sample below shows a partial listing of the 1-D cross sections.
Following the 1-D cross section listing is the scattering matrix for the
nuclide. This abbreviated listing shows a portion of the
P\ h jhhh!NhNubj)}(h:sub:`0`h]h/0}(hhh jubah}(h]h]h]h]h]uhjh jubh/e matrix for this nuclide; however, in a full listing, all
higher-order elements are printed as well.}(he matrix for this nuclide; however, in a full listing, all
higher-order elements are printed as well.h jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jhhubhM)}(hAs was indicated in the input description, specification of
*prtxsec*\ =1d can be used to obtain header and 1‑D cross section data
only, skipping the printing of scattering matrices.h](h/ =1d can be used to skip the printing of scattering matrices.}(h>\ =1d can be used to skip the printing of scattering matrices.h j*hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jhhubh)}(h.. _fig9-2-70:h]h}(h]h]h]h]h]h fig9-2-70uhh
hMh jhhh!h"ubj)}(hhh](j)}(hx.. figure:: figs/NEWT/fig70.svg
:align: center
:width: 1000
Partial listing of Mixture Cross section data pages.
h]h}(h]h]h]h]h]width1000urifigs/NEWT/fig70.svgj*}j,jgsuhjh jWh!h"hMubj.)}(h4Partial listing of Mixture Cross section data pages.h]h/4Partial listing of Mixture Cross section data pages.}(hjkh jiubah}(h]h]h]h]h]uhj-h!h"hMh jWubeh}(h](id230jVeh]h] fig9-2-70ah]h]jEcenteruhjhMh jhhh!h"j}j|jLsj}jVjLsubh)}(h.. _9-2-5-3:h]h}(h]h]h]h]h]hid141uhh
hMh jhhh!h"ubeh}(h](mixture-cross-sectionsjeh]h](mixture cross sections
9-2-5-2-15eh]h]uhh#h jchhh!h"hMj}jjsj}jjsubeh}(h](
input-summaryjWeh]h](
input summary9-2-5-2eh]h]uhh#h jhhh!h"hMj}jjMsj}jWjMsubh$)}(hhh](h))}(hIteration historyh]h/Iteration history}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hMubhM)}(hXThe next portion of NEWT output lists the iteration convergence
history for the iterative solution
(:numref:`fig9-2-71`). This information can be used to track and understand
the performance of the outer loop of the iterative solution. The first
column provides the outer iteration count. The second column lists the
system eigenvalue after each outer iteration. The third column lists
the change in the eigenvalue from the last outer iteration; this is
one of the parameters tested for convergence. The fourth column, “Max
Flux Delta,” gives the maximum change in cell flux for all cells and
all energy groups; this is also used as a convergence test. The next
column lists the cell number and energy group corresponding to the
maximum flux change in this iteration. The next two columns list the
same flux information for mixtures with fissionable nuclides. This can
be used to track spatial convergence in fuel when convergence is
slowed by significant scattering outside the fuel. Finally, the last
column provides information on the convergence of inners in each outer
iteration. Inner iterations do not need to converge within early outer
iterations, but final convergence will not be achieved until all
inners are converged. The maximum number of inner iterations per
energy group is set by the *inners=* parameter in the parameter input
block. After convergence is achieved, the table is terminated by
printing the final version of *k*\ :sub:`eff`.h](h/dThe next portion of NEWT output lists the iteration convergence
history for the iterative solution
(}(hdThe next portion of NEWT output lists the iteration convergence
history for the iterative solution
(h jhhh!NhNubj)}(h:numref:`fig9-2-71`h]jM)}(hjh]h/ fig9-2-71}(hhh jubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainj˗reftypenumrefrefexplicitrefwarnjW fig9-2-71uhjh!h"hMh jubh/X). This information can be used to track and understand
the performance of the outer loop of the iterative solution. The first
column provides the outer iteration count. The second column lists the
system eigenvalue after each outer iteration. The third column lists
the change in the eigenvalue from the last outer iteration; this is
one of the parameters tested for convergence. The fourth column, “Max
Flux Delta,” gives the maximum change in cell flux for all cells and
all energy groups; this is also used as a convergence test. The next
column lists the cell number and energy group corresponding to the
maximum flux change in this iteration. The next two columns list the
same flux information for mixtures with fissionable nuclides. This can
be used to track spatial convergence in fuel when convergence is
slowed by significant scattering outside the fuel. Finally, the last
column provides information on the convergence of inners in each outer
iteration. Inner iterations do not need to converge within early outer
iterations, but final convergence will not be achieved until all
inners are converged. The maximum number of inner iterations per
energy group is set by the }(hX). This information can be used to track and understand
the performance of the outer loop of the iterative solution. The first
column provides the outer iteration count. The second column lists the
system eigenvalue after each outer iteration. The third column lists
the change in the eigenvalue from the last outer iteration; this is
one of the parameters tested for convergence. The fourth column, “Max
Flux Delta,” gives the maximum change in cell flux for all cells and
all energy groups; this is also used as a convergence test. The next
column lists the cell number and energy group corresponding to the
maximum flux change in this iteration. The next two columns list the
same flux information for mixtures with fissionable nuclides. This can
be used to track spatial convergence in fuel when convergence is
slowed by significant scattering outside the fuel. Finally, the last
column provides information on the convergence of inners in each outer
iteration. Inner iterations do not need to converge within early outer
iterations, but final convergence will not be achieved until all
inners are converged. The maximum number of inner iterations per
energy group is set by the h jhhh!NhNubj)}(h *inners=*h]h/inners=}(hhh jubah}(h]h]h]h]h]uhjh jubh/ parameter in the parameter input
block. After convergence is achieved, the table is terminated by
printing the final version of }(h parameter in the parameter input
block. After convergence is achieved, the table is terminated by
printing the final version of h jhhh!NhNubj)}(h*k*h]h/k}(hhh jubah}(h]h]h]h]h]uhjh jubh/ }(h\ h jhhh!NhNubj)}(h
:sub:`eff`h]h/eff}(hhh jubah}(h]h]h]h]h]uhjh jubh/.}(hhh jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jhhubhM)}(hXIf the parameter keyword *timed=* is set to *yes*, four additional
columns are introduced that give timing information on the solution
process, listing real (“wall clock”) time, elapsed CPU time since
beginning the iteration process, elapsed CPU time per outer iteration,
and an estimate of the fractional CPU usage during each outer.
:numref:`fig9-2-72` illustrates the form of output produced when *timed=yes*
is input. Additionally, a supplementary edit follows the iteration edit
when *timed=yes*, giving information on average time per transport sweep
(outer iteration) within different components of the solution. This edit
is especially useful when coarse-mesh finite-difference acceleration is
used, to assess the overhead of the CMFD accelerator.h](h/If the parameter keyword }(hIf the parameter keyword h j hhh!NhNubj)}(h*timed=*h]h/timed=}(hhh j)ubah}(h]h]h]h]h]uhjh j ubh/ is set to }(h is set to h j hhh!NhNubj)}(h*yes*h]h/yes}(hhh j<ubah}(h]h]h]h]h]uhjh j ubh/X", four additional
columns are introduced that give timing information on the solution
process, listing real (“wall clock”) time, elapsed CPU time since
beginning the iteration process, elapsed CPU time per outer iteration,
and an estimate of the fractional CPU usage during each outer.
}(hX", four additional
columns are introduced that give timing information on the solution
process, listing real (“wall clock”) time, elapsed CPU time since
beginning the iteration process, elapsed CPU time per outer iteration,
and an estimate of the fractional CPU usage during each outer.
h j hhh!NhNubj)}(h:numref:`fig9-2-72`h]jM)}(hjQh]h/ fig9-2-72}(hhh jSubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jOubah}(h]h]h]h]h]refdochj refdomainj]reftypenumrefrefexplicitrefwarnjW fig9-2-72uhjh!h"hMh j ubh/. illustrates the form of output produced when }(h. illustrates the form of output produced when h j hhh!NhNubj)}(h*timed=yes*h]h/ timed=yes}(hhh jtubah}(h]h]h]h]h]uhjh j ubh/N
is input. Additionally, a supplementary edit follows the iteration edit
when }(hN
is input. Additionally, a supplementary edit follows the iteration edit
when h j hhh!NhNubj)}(h*timed=yes*h]h/ timed=yes}(hhh jubah}(h]h]h]h]h]uhjh j ubh/, giving information on average time per transport sweep
(outer iteration) within different components of the solution. This edit
is especially useful when coarse-mesh finite-difference acceleration is
used, to assess the overhead of the CMFD accelerator.}(h, giving information on average time per transport sweep
(outer iteration) within different components of the solution. This edit
is especially useful when coarse-mesh finite-difference acceleration is
used, to assess the overhead of the CMFD accelerator.h j hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jhhubh)}(h.. _fig9-2-71:h]h}(h]h]h]h]h]h fig9-2-71uhh
hM!h jhhh!h"ubj)}(hhh](j)}(he.. figure:: figs/NEWT/fig71.svg
:align: center
:width: 600
Nominal iteration history output.
h]h}(h]h]h]h]h]width600urifigs/NEWT/fig71.svgj*}j,jsuhjh jh!h"hM&ubj.)}(h!Nominal iteration history output.h]h/!Nominal iteration history output.}(hjh jubah}(h]h]h]h]h]uhj-h!h"hM&h jubeh}(h](id231jeh]h] fig9-2-71ah]h]jEcenteruhjhM&h jhhh!h"j}jИjsj}jjsubh)}(h.. _fig9-2-72:h]h}(h]h]h]h]h]h fig9-2-72uhh
hM)h jhhh!h"ubj)}(hhh](j)}(hb.. figure:: figs/NEWT/fig72.svg
:align: center
:width: 600
Timed iteration history output.
h]h}(h]h]h]h]h]width600urifigs/NEWT/fig72.svgj*}j,jsuhjh jh!h"hM.ubj.)}(hTimed iteration history output.h]h/Timed iteration history output.}(hjh jubah}(h]h]h]h]h]uhj-h!h"hM.h jubeh}(h](id232jeh]h] fig9-2-72ah]h]jEcenteruhjhM.h jhhh!h"j}jj֘sj}jj֘subh)}(h.. _9-2-5-4:h]h}(h]h]h]h]h]hid142uhh
hM0h jhhh!h"ubeh}(h](iteration-historyjeh]h](iteration history9-2-5-3eh]h]uhh#h jhhh!h"hMj}jjsj}jjsubh$)}(hhh](h))}(hFour-factor formulah]h/Four-factor formula}(hj'h j%hhh!NhNubah}(h]h]h]h]h]uhh(h j"hhh!h"hM3ubhM)}(hXFollowing the iteration history listing, NEWT output provides edit
listing the four traditional components of the four-factor formula. This
is followed by an alternate three-group formulation that separates out
resonance and fast escape probabilities (:numref:`fig9-2-73`).h](h/Following the iteration history listing, NEWT output provides edit
listing the four traditional components of the four-factor formula. This
is followed by an alternate three-group formulation that separates out
resonance and fast escape probabilities (
}(hFollowing the iteration history listing, NEWT output provides edit
listing the four traditional components of the four-factor formula. This
is followed by an alternate three-group formulation that separates out
resonance and fast escape probabilities (h j3hhh!NhNubj)}(h:numref:`fig9-2-73`h]jM)}(hj>h]h/ fig9-2-73}(hhh j@ubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh j<ubah}(h]h]h]h]h]refdochj refdomainjJreftypenumrefrefexplicitrefwarnjW fig9-2-73uhjh!h"hM5h j3ubh/).}(h).h j3hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM5h j"hhubh)}(h.. _fig9-2-73:h]h}(h]h]h]h]h]h fig9-2-73uhh
hM:h j"hhh!h"ubj)}(hhh](j)}(h~.. figure:: figs/NEWT/fig73.svg
:align: center
:width: 500
Four-factor formula with alternate three-group formulation.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig73.svgj*}j,jsuhjh jrh!h"hM?ubj.)}(h;Four-factor formula with alternate three-group formulation.h]h/;Four-factor formula with alternate three-group formulation.}(hjh jubah}(h]h]h]h]h]uhj-h!h"hM?h jrubeh}(h](id233jqeh]h] fig9-2-73ah]h]jEcenteruhjhM?h j"hhh!h"j}jjgsj}jqjgsubh)}(h.. _9-2-5-5:h]h}(h]h]h]h]h]hid143uhh
hMAh j"hhh!h"ubeh}(h](four-factor-formulajeh]h](four-factor formula9-2-5-4eh]h]uhh#h jhhh!h"hM3j}jjsj}jjsubh$)}(hhh](h))}(hFine-group balance tablesh]h/Fine-group balance tables}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hMDubhM)}(hXWFollowing the iteration history and flux convergence, a fine-group
balance table is provided for each mixture used in the calculation. Fine
group refers to the group structure of the library used for the
calculation. Broad-group data, discussed later, refer to a group
structure collapsed from the original fine-group structure. After tables
for all mixtures are printed, a last table provides a fine-group summary
for the entire problem (i.e., the volume-weighted average for all
mixtures). Balance tables are printed by default but may be disabled by
setting *prtbalnc=no* in the Parameter block.h](h/X2Following the iteration history and flux convergence, a fine-group
balance table is provided for each mixture used in the calculation. Fine
group refers to the group structure of the library used for the
calculation. Broad-group data, discussed later, refer to a group
structure collapsed from the original fine-group structure. After tables
for all mixtures are printed, a last table provides a fine-group summary
for the entire problem (i.e., the volume-weighted average for all
mixtures). Balance tables are printed by default but may be disabled by
setting }(hX2Following the iteration history and flux convergence, a fine-group
balance table is provided for each mixture used in the calculation. Fine
group refers to the group structure of the library used for the
calculation. Broad-group data, discussed later, refer to a group
structure collapsed from the original fine-group structure. After tables
for all mixtures are printed, a last table provides a fine-group summary
for the entire problem (i.e., the volume-weighted average for all
mixtures). Balance tables are printed by default but may be disabled by
setting h jęhhh!NhNubj)}(h
*prtbalnc=no*h]h/prtbalnc=no}(hhh j͙ubah}(h]h]h]h]h]uhjh jęubh/ in the Parameter block.}(h in the Parameter block.h jęhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMFh jhhubhM)}(hX:numref:`fig9-2-74` shows a clipped excerpt from the fine-group summary of an
output listing. Similar tables are produced for each mixture in the
problem for all energy groups in the problem. The header lists the NEWT
mixture number; the mixture ID (i.e., the SCALE mixture number); and the
mixture description, if provided in the original input specification.
The header also gives the number of computational cells in which the
mixture was present and the volume of the mixture in the problem.h](j)}(h:numref:`fig9-2-74`h]jM)}(hjh]h/ fig9-2-74}(hhh jubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjreftypenumrefrefexplicitrefwarnjW fig9-2-74uhjh!h"hMPh jubh/X shows a clipped excerpt from the fine-group summary of an
output listing. Similar tables are produced for each mixture in the
problem for all energy groups in the problem. The header lists the NEWT
mixture number; the mixture ID (i.e., the SCALE mixture number); and the
mixture description, if provided in the original input specification.
The header also gives the number of computational cells in which the
mixture was present and the volume of the mixture in the problem.}(hX shows a clipped excerpt from the fine-group summary of an
output listing. Similar tables are produced for each mixture in the
problem for all energy groups in the problem. The header lists the NEWT
mixture number; the mixture ID (i.e., the SCALE mixture number); and the
mixture description, if provided in the original input specification.
The header also gives the number of computational cells in which the
mixture was present and the volume of the mixture in the problem.h jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMPh jhhubhM)}(hXFor each mixture, two tables are printed. The first table provides a
balance of all sources and loss terms: the fixed source, the fission
source, in-scatter, out-scatter, absorption, leakage, n-2n production,
and the net balance of all terms for each energy group. The final row
lists the mixture total for all groups. The fixed source lists the
user-supplied source for fixed-source problems. This field is disabled
(set to zero) for eigenvalue calculations. The fission source is the
number of neutrons born into each energy group in the mixture. In this
example, the mixture is water, which is not fissile; hence, no fission
source is present. In‑scatter represents the number of neutrons
scattered into each group from all other groups; conversely, out‑scatter
is the loss from each energy group by scattering. Absorption is the
number of neutrons absorbed in reactions that do not emit a neutron
(e.g., n-γ). Leakage is the net loss of neutrons from the mixture to
another mixture or a nonreflective boundary, and n-2n is the effective
n-2n production rate calculated from a weighted sum of all n-\ *x*\ n
reactions. The balance table is the ratio of production to loss in each
energy group.h](h/XVFor each mixture, two tables are printed. The first table provides a
balance of all sources and loss terms: the fixed source, the fission
source, in-scatter, out-scatter, absorption, leakage, n-2n production,
and the net balance of all terms for each energy group. The final row
lists the mixture total for all groups. The fixed source lists the
user-supplied source for fixed-source problems. This field is disabled
(set to zero) for eigenvalue calculations. The fission source is the
number of neutrons born into each energy group in the mixture. In this
example, the mixture is water, which is not fissile; hence, no fission
source is present. In‑scatter represents the number of neutrons
scattered into each group from all other groups; conversely, out‑scatter
is the loss from each energy group by scattering. Absorption is the
number of neutrons absorbed in reactions that do not emit a neutron
(e.g., n-γ). Leakage is the net loss of neutrons from the mixture to
another mixture or a nonreflective boundary, and n-2n is the effective
n-2n production rate calculated from a weighted sum of all n- }(hXVFor each mixture, two tables are printed. The first table provides a
balance of all sources and loss terms: the fixed source, the fission
source, in-scatter, out-scatter, absorption, leakage, n-2n production,
and the net balance of all terms for each energy group. The final row
lists the mixture total for all groups. The fixed source lists the
user-supplied source for fixed-source problems. This field is disabled
(set to zero) for eigenvalue calculations. The fission source is the
number of neutrons born into each energy group in the mixture. In this
example, the mixture is water, which is not fissile; hence, no fission
source is present. In‑scatter represents the number of neutrons
scattered into each group from all other groups; conversely, out‑scatter
is the loss from each energy group by scattering. Absorption is the
number of neutrons absorbed in reactions that do not emit a neutron
(e.g., n-γ). Leakage is the net loss of neutrons from the mixture to
another mixture or a nonreflective boundary, and n-2n is the effective
n-2n production rate calculated from a weighted sum of all n-\ h jhhh!NhNubj)}(h*x*h]h/x}(hhh jubah}(h]h]h]h]h]uhjh jubh/Y n
reactions. The balance table is the ratio of production to loss in each
energy group.}(hY\ n
reactions. The balance table is the ratio of production to loss in each
energy group.h jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMXh jhhubhM)}(hXThe second fine-group balance table, also shown in Figure 9.2.74, lists
other reactions rates of interest. The first two columns after the group
number list in-scatter broken into its upscatter and downscatter
components. The subsequent two columns provide a similar breakdown for
out-scatter from the energy group. Self-scatter is the amount of
within-group scattering occurring within each energy group. The fission
rate is the number of (n-fission) reactions occurring in each group. The
next column provides the transverse leakage (i.e., the product of the
flux and the DB\ :sup:`2` term). This column will provide only nonzero
values when a nonzero buckling height is specified in input. The final
column lists the total (scalar) flux for each energy group.h](h/XDThe second fine-group balance table, also shown in Figure 9.2.74, lists
other reactions rates of interest. The first two columns after the group
number list in-scatter broken into its upscatter and downscatter
components. The subsequent two columns provide a similar breakdown for
out-scatter from the energy group. Self-scatter is the amount of
within-group scattering occurring within each energy group. The fission
rate is the number of (n-fission) reactions occurring in each group. The
next column provides the transverse leakage (i.e., the product of the
flux and the DB }(hXDThe second fine-group balance table, also shown in Figure 9.2.74, lists
other reactions rates of interest. The first two columns after the group
number list in-scatter broken into its upscatter and downscatter
components. The subsequent two columns provide a similar breakdown for
out-scatter from the energy group. Self-scatter is the amount of
within-group scattering occurring within each energy group. The fission
rate is the number of (n-fission) reactions occurring in each group. The
next column provides the transverse leakage (i.e., the product of the
flux and the DB\ h j7hhh!NhNubjY)}(h:sup:`2`h]h/2}(hhh j@ubah}(h]h]h]h]h]uhjXh j7ubh/ term). This column will provide only nonzero
values when a nonzero buckling height is specified in input. The final
column lists the total (scalar) flux for each energy group.}(h term). This column will provide only nonzero
values when a nonzero buckling height is specified in input. The final
column lists the total (scalar) flux for each energy group.h j7hhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMkh jhhubh)}(h.. _fig9-2-74:h]h}(h]h]h]h]h]h fig9-2-74uhh
hMxh jhhh!h"ubj)}(hhh](j)}(ht.. figure:: figs/NEWT/fig74.svg
:align: center
:width: 1000
Partial mixture fine-group balance table output.
h]h}(h]h]h]h]h]width1000urifigs/NEWT/fig74.svgj*}j,jtsuhjh jdh!h"hM}ubj.)}(h0Partial mixture fine-group balance table output.h]h/0Partial mixture fine-group balance table output.}(hjxh jvubah}(h]h]h]h]h]uhj-h!h"hM}h jdubeh}(h](id234jceh]h] fig9-2-74ah]h]jEcenteruhjhM}h jhhh!h"j}jjYsj}jcjYsubh)}(h.. _9-2-5-6:h]h}(h]h]h]h]h]hid144uhh
hMh jhhh!h"ubeh}(h](fine-group-balance-tablesjeh]h](fine-group balance tables9-2-5-5eh]h]uhh#h jhhh!h"hMDj}jjsj}jjsubh$)}(hhh](h))}(hPlanar fluxes and currentsh]h/Planar fluxes and currents}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hMubhM)}(hX<If planar fluxes are requested, an edit is printed to provide fluxes and
currents on each line segment specified, identified by label
(:numref:`fig9-2-75`). Fine-group fluxes are listed for each energy group,
followed by x and y net currents and partial currents (+x, –x, +y, and
–y). Fluxes and currents are printed for each group in the input group
structure. The example below shows only partial listings of each for
simplicity. If a broad-group collapse is requested, the fine-group
output is followed by the set of fluxes and currents for each broad
energy group.h](h/If planar fluxes are requested, an edit is printed to provide fluxes and
currents on each line segment specified, identified by label
(}(hIf planar fluxes are requested, an edit is printed to provide fluxes and
currents on each line segment specified, identified by label
(h jhhh!NhNubj)}(h:numref:`fig9-2-75`h]jM)}(hjh]h/ fig9-2-75}(hhh jÚubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainj͚reftypenumrefrefexplicitrefwarnjW fig9-2-75uhjh!h"hMh jubh/X). Fine-group fluxes are listed for each energy group,
followed by x and y net currents and partial currents (+x, –x, +y, and
–y). Fluxes and currents are printed for each group in the input group
structure. The example below shows only partial listings of each for
simplicity. If a broad-group collapse is requested, the fine-group
output is followed by the set of fluxes and currents for each broad
energy group.}(hX). Fine-group fluxes are listed for each energy group,
followed by x and y net currents and partial currents (+x, –x, +y, and
–y). Fluxes and currents are printed for each group in the input group
structure. The example below shows only partial listings of each for
simplicity. If a broad-group collapse is requested, the fine-group
output is followed by the set of fluxes and currents for each broad
energy group.h jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jhhubhM)}(hNote that discontinuity factors make internal use of planar fluxes to
determine the flux and current on each boundary. Hence, planar flux
edits will be present any time an ADF calculation is performed.h]h/Note that discontinuity factors make internal use of planar fluxes to
determine the flux and current on each boundary. Hence, planar flux
edits will be present any time an ADF calculation is performed.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMh jhhubh)}(h.. _fig9-2-75:h]h}(h]h]h]h]h]h fig9-2-75uhh
hMh jhhh!h"ubj)}(hhh](j)}(h.. figure:: figs/NEWT/fig75.svg
:align: center
:width: 600
Example of planar flux and current output (continued below).
h]h}(h]h]h]h]h]width600urifigs/NEWT/fig75.svgj*}j,jsuhjh jh!h"hMubj.)}(hsuhjh j.h!h"hM,ubj.)}(hSPartial collapsing spectra listing for a case with no critical buckling correction.h]h/SPartial collapsing spectra listing for a case with no critical buckling correction.}(hjBh j@ubah}(h]h]h]h]h]uhj-h!h"hM,h j.ubeh}(h](id241j-eh]h] fig9-2-81ah]h]jEcenteruhjhM,h jޞhhh!h"j}jSj#sj}j-j#subh)}(h
.. _9-2-5-12:h]h}(h]h]h]h]h]hid154uhh
hM.h jޞhhh!h"ubh$)}(hhh](h))}(hHomogenized cross sectionsh]h/Homogenized cross sections}(hjih jghhh!NhNubah}(h]h]h]h]h]uhh(h jdhhh!h"hM1ubhM)}(hXWhen homogenization is performed and parameter *prthmmix=yes* is set,
the final output section of a NEWT calculation is the homogenized cross
section edit, as shown in :numref:`fig9-2-82`. This information is generally
passed to nodal analysis codes and hence is presented in a slightly
different format from other cross sections. Output includes a
region-averaged k-infinity value, transport-corrected cross section, and
two interpretations of absorption. The first is the directly collapsed
absorption cross section, while the second (Total-Scatter) is a more
consistent definition of absorption as applied in nodal calculations.
The difference between the two definitions is the effective (n-2n)
cross section. Both cross sections exclude contributions from
:sup:`135`\ Xe and :sup:`149`\ Sm; microscopic cross sections and number
densities for these two nuclides are printed explicitly elsewhere in the
table. Nu*fission is the product of the fission cross section and the
number of neutrons produced per fission, while Kappa*fission is the
product of the fission cross section and the energy release per fission
(J). Inverse velocity is the inverse (1/x) of the group neutron speed.h](h//When homogenization is performed and parameter }(h/When homogenization is performed and parameter h juhhh!NhNubj)}(h*prthmmix=yes*h]h/prthmmix=yes}(hhh j~ubah}(h]h]h]h]h]uhjh juubh/k is set,
the final output section of a NEWT calculation is the homogenized cross
section edit, as shown in }(hk is set,
the final output section of a NEWT calculation is the homogenized cross
section edit, as shown in h juhhh!NhNubj)}(h:numref:`fig9-2-82`h]jM)}(hjh]h/ fig9-2-82}(hhh jubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjreftypenumrefrefexplicitrefwarnjW fig9-2-82uhjh!h"hM3h juubh/XC. This information is generally
passed to nodal analysis codes and hence is presented in a slightly
different format from other cross sections. Output includes a
region-averaged k-infinity value, transport-corrected cross section, and
two interpretations of absorption. The first is the directly collapsed
absorption cross section, while the second (Total-Scatter) is a more
consistent definition of absorption as applied in nodal calculations.
The difference between the two definitions is the effective (n-2n)
cross section. Both cross sections exclude contributions from
}(hXC. This information is generally
passed to nodal analysis codes and hence is presented in a slightly
different format from other cross sections. Output includes a
region-averaged k-infinity value, transport-corrected cross section, and
two interpretations of absorption. The first is the directly collapsed
absorption cross section, while the second (Total-Scatter) is a more
consistent definition of absorption as applied in nodal calculations.
The difference between the two definitions is the effective (n-2n)
cross section. Both cross sections exclude contributions from
h juhhh!NhNubjY)}(h
:sup:`135`h]h/135}(hhh jubah}(h]h]h]h]h]uhjXh juubh/ Xe and }(h \ Xe and h juhhh!NhNubjY)}(h
:sup:`149`h]h/149}(hhh jɟubah}(h]h]h]h]h]uhjXh juubh/X Sm; microscopic cross sections and number
densities for these two nuclides are printed explicitly elsewhere in the
table. Nu*fission is the product of the fission cross section and the
number of neutrons produced per fission, while Kappa*fission is the
product of the fission cross section and the energy release per fission
(J). Inverse velocity is the inverse (1/x) of the group neutron speed.}(hX\ Sm; microscopic cross sections and number
densities for these two nuclides are printed explicitly elsewhere in the
table. Nu*fission is the product of the fission cross section and the
number of neutrons produced per fission, while Kappa*fission is the
product of the fission cross section and the energy release per fission
(J). Inverse velocity is the inverse (1/x) of the group neutron speed.h juhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hM3h jdhhubhM)}(hThe table also lists the two-group isotropic scattering matrix and the
prompt fission fraction distribution. Finally, NEWT lists approximate
six-group decay constants (lambdas) and group fractions (betas) for each
group.h]h/The table also lists the two-group isotropic scattering matrix and the
prompt fission fraction distribution. Finally, NEWT lists approximate
six-group decay constants (lambdas) and group fractions (betas) for each
group.}(hjh jhhh!NhNubah}(h]h]h]h]h]uhhLh!h"hMEh jdhhubh)}(h.. _fig9-2-82:h]h}(h]h]h]h]h]h fig9-2-82uhh
hMJh jdhhh!h"ubj)}(hhh](j)}(h.. figure:: figs/NEWT/fig82.svg
:align: center
:width: 1000
Homogenized cross section edit for nodal diffusion applications.
h]h}(h]h]h]h]h]width1000urifigs/NEWT/fig82.svgj*}j,jsuhjh jh!h"hMOubj.)}(h@Homogenized cross section edit for nodal diffusion applications.h]h/@Homogenized cross section edit for nodal diffusion applications.}(hjh j
ubah}(h]h]h]h]h]uhj-h!h"hMOh jubeh}(h](id242jeh]h] fig9-2-82ah]h]jEcenteruhjhMOh jdhhh!h"j}j jsj}jjsubh)}(h
.. _9-2-5-13:h]h}(h]h]h]h]h]hid155uhh
hMQh jdhhh!h"ubeh}(h](homogenized-cross-sectionsjceh]h](homogenized cross sections9-2-5-12eh]h]uhh#h jޞhhh!h"hM1j}j7jYsj}jcjYsubeh}(h](groupwise-form-factorsjҞeh]h](groupwise form factors9-2-5-11eh]h]uhh#h jhhh!h"hM j}jBjȞsj}jҞjȞsubh$)}(hhh](h))}(hEnd-of-calculation bannerh]h/End-of-calculation banner}(hjLh jJhhh!NhNubah}(h]h]h]h]h]uhh(h jGhhh!h"hMTubhM)}(hXNEWT output listings are terminated with an end-of-calculation banner
(shown in :numref:`fig9-2-83`) upon successful completion of a calculation. If
this banner is not present, then the calculation ended abnormally, and
the output listing must be reviewed to determine the cause of the error.
In general, the final lines of an output file describe the error
condition that caused the calculation to stop.h](h/PNEWT output listings are terminated with an end-of-calculation banner
(shown in }(hPNEWT output listings are terminated with an end-of-calculation banner
(shown in h jXhhh!NhNubj)}(h:numref:`fig9-2-83`h]jM)}(hjch]h/ fig9-2-83}(hhh jeubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jaubah}(h]h]h]h]h]refdochj refdomainjoreftypenumrefrefexplicitrefwarnjW fig9-2-83uhjh!h"hMVh jXubh/X1) upon successful completion of a calculation. If
this banner is not present, then the calculation ended abnormally, and
the output listing must be reviewed to determine the cause of the error.
In general, the final lines of an output file describe the error
condition that caused the calculation to stop.}(hX1) upon successful completion of a calculation. If
this banner is not present, then the calculation ended abnormally, and
the output listing must be reviewed to determine the cause of the error.
In general, the final lines of an output file describe the error
condition that caused the calculation to stop.h jXhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMVh jGhhubh)}(h.. _fig9-2-83:h]h}(h]h]h]h]h]h fig9-2-83uhh
hM]h jGhhh!h"ubj)}(hhh](j)}(he.. figure:: figs/NEWT/fig83.svg
:align: center
:width: 800
End-of-calculation banner listing.
h]h}(h]h]h]h]h]width800urifigs/NEWT/fig83.svgj*}j,jsuhjh jh!h"hMbubj.)}(h"End-of-calculation banner listing.h]h/"End-of-calculation banner listing.}(hjh jubah}(h]h]h]h]h]uhj-h!h"hMbh jubeh}(h](id243jeh]h] fig9-2-83ah]h]jEcenteruhjhMbh jGhhh!h"j}jjsj}jjsubh)}(h
.. _9-2-5-14:h]h}(h]h]h]h]h]hid156uhh
hMdh jGhhh!h"ubh$)}(hhh](h))}(hPostscript graphics filesh]h/Postscript graphics files}(hjҠh jРhhh!NhNubah}(h]h]h]h]h]uhh(h j͠hhh!h"hMgubhM)}(hXrTwo user-selectable options within NEWT provide the ability to generate
PostScript-based graphics files for visualization of both input
specifications and output results. By specification of *drawit=yes* in
the NEWT parameter block, NEWT will generate two PostScript-based plot
files: :file:`newtgrid.ps` and :file:`newtmatl.ps`. The former, a grayscale plot of the
line segments generated by NEWT based on the input specification, will
be generated if all body placement input is valid. If input contains
errors such that the code stops before grid generation routines are
completed, no :file:`newtgrid.ps` output is created.h](h/Two user-selectable options within NEWT provide the ability to generate
PostScript-based graphics files for visualization of both input
specifications and output results. By specification of }(hTwo user-selectable options within NEWT provide the ability to generate
PostScript-based graphics files for visualization of both input
specifications and output results. By specification of h jޠhhh!NhNubj)}(h*drawit=yes*h]h/
drawit=yes}(hhh jubah}(h]h]h]h]h]uhjh jޠubh/R in
the NEWT parameter block, NEWT will generate two PostScript-based plot
files: }(hR in
the NEWT parameter block, NEWT will generate two PostScript-based plot
files: h jޠhhh!NhNubjM)}(h:file:`newtgrid.ps`h]h/newtgrid.ps}(hnewtgrid.psh jubah}(h]h]fileah]h]h]rolefileuhjLh jޠubh/ and }(h and h jޠhhh!NhNubjM)}(h:file:`newtmatl.ps`h]h/newtmatl.ps}(hnewtmatl.psh jubah}(h]h]fileah]h]h]rolefileuhjLh jޠubh/X. The former, a grayscale plot of the
line segments generated by NEWT based on the input specification, will
be generated if all body placement input is valid. If input contains
errors such that the code stops before grid generation routines are
completed, no }(hX. The former, a grayscale plot of the
line segments generated by NEWT based on the input specification, will
be generated if all body placement input is valid. If input contains
errors such that the code stops before grid generation routines are
completed, no h jޠhhh!NhNubjM)}(h:file:`newtgrid.ps`h]h/newtgrid.ps}(hnewtgrid.psh j(ubah}(h]h]fileah]h]h]rolefileuhjLh jޠubh/ output is created.}(h output is created.h jޠhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMih j͠hhubhM)}(hXYThe :file:`newtmatl.ps` plot illustrates the same grid structure but with
material placement indicated by color. At this time, no user control is
provided for color assignment or plot control. This plot also requires
complete grid generation; additionally, it requires completion of all
media placement routines before the plot will be produced.h](h/The }(hThe h jEhhh!NhNubjM)}(h:file:`newtmatl.ps`h]h/newtmatl.ps}(hnewtmatl.psh jNubah}(h]h]fileah]h]h]rolefileuhjLh jEubh/XB plot illustrates the same grid structure but with
material placement indicated by color. At this time, no user control is
provided for color assignment or plot control. This plot also requires
complete grid generation; additionally, it requires completion of all
media placement routines before the plot will be produced.}(hXB plot illustrates the same grid structure but with
material placement indicated by color. At this time, no user control is
provided for color assignment or plot control. This plot also requires
complete grid generation; additionally, it requires completion of all
media placement routines before the plot will be produced.h jEhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMsh j͠hhubhM)}(hXEFigures used throughout this manual were generated from newtgrid and
newtmatl PostScript plot files. Files :file:`newtgrid.ps` and :file:`newtmatl.ps` are
automatically copied back from SCALE’s temporary directory to the
original location of the input case, with the names
*casename*.newtgrid.ps and *casename*.newtmatl.ps.h](h/kFigures used throughout this manual were generated from newtgrid and
newtmatl PostScript plot files. Files }(hkFigures used throughout this manual were generated from newtgrid and
newtmatl PostScript plot files. Files h jkhhh!NhNubjM)}(h:file:`newtgrid.ps`h]h/newtgrid.ps}(hnewtgrid.psh jtubah}(h]h]fileah]h]h]rolefileuhjLh jkubh/ and }(h and h jkhhh!NhNubjM)}(h:file:`newtmatl.ps`h]h/newtmatl.ps}(hnewtmatl.psh jubah}(h]h]fileah]h]h]rolefileuhjLh jkubh/} are
automatically copied back from SCALE’s temporary directory to the
original location of the input case, with the names
}(h} are
automatically copied back from SCALE’s temporary directory to the
original location of the input case, with the names
h jkhhh!NhNubj)}(h
*casename*h]h/casename}(hhh jubah}(h]h]h]h]h]uhjh jkubh/.newtgrid.ps and }(h.newtgrid.ps and h jkhhh!NhNubj)}(h
*casename*h]h/casename}(hhh jubah}(h]h]h]h]h]uhjh jkubh/
.newtmatl.ps.}(h
.newtmatl.ps.h jkhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMyh j͠hhubhM)}(hXWhen *prtflux=yes* is input, NEWT will generate a set of flux plots
showing relative neutron number densities in each energy group. A plot
file will be generated with the name fluxplot\_\ *N*\ g.ps, where *N* is
the number of energy groups in the problem. If an energy collapse is
performed, an additional file named fluxplot\_\ *M*\ g.ps is created,
where M is the number of energy groups in the collapsed set.
:numref:`fig9-2-84` is an example of a flux plot output for the fast group of
a two-group flux collapse.h](h/When }(hWhen h jΡhhh!NhNubj)}(h
*prtflux=yes*h]h/prtflux=yes}(hhh jסubah}(h]h]h]h]h]uhjh jΡubh/ is input, NEWT will generate a set of flux plots
showing relative neutron number densities in each energy group. A plot
file will be generated with the name fluxplot_ }(h is input, NEWT will generate a set of flux plots
showing relative neutron number densities in each energy group. A plot
file will be generated with the name fluxplot\_\ h jΡhhh!NhNubj)}(h*N*h]h/N}(hhh jubah}(h]h]h]h]h]uhjh jΡubh/ g.ps, where }(h\ g.ps, where h jΡhhh!NhNubj)}(h*N*h]h/N}(hhh jubah}(h]h]h]h]h]uhjh jΡubh/y is
the number of energy groups in the problem. If an energy collapse is
performed, an additional file named fluxplot_ }(hy is
the number of energy groups in the problem. If an energy collapse is
performed, an additional file named fluxplot\_\ h jΡhhh!NhNubj)}(h*M*h]h/M}(hhh jubah}(h]h]h]h]h]uhjh jΡubh/P g.ps is created,
where M is the number of energy groups in the collapsed set.
}(hP\ g.ps is created,
where M is the number of energy groups in the collapsed set.
h jΡhhh!NhNubj)}(h:numref:`fig9-2-84`h]jM)}(hj%h]h/ fig9-2-84}(hhh j'ubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh j#ubah}(h]h]h]h]h]refdochj refdomainj1reftypenumrefrefexplicitrefwarnjW fig9-2-84uhjh!h"hMh jΡubh/U is an example of a flux plot output for the fast group of
a two-group flux collapse.}(hU is an example of a flux plot output for the fast group of
a two-group flux collapse.h jΡhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh j͠hhubh)}(h.. _fig9-2-84:h]h}(h]h]h]h]h]h fig9-2-84uhh
hMh j͠hhh!h"ubj)}(hhh](j)}(hy.. figure:: figs/NEWT/fig84.png
:align: center
:width: 600
Example of a flux plot image created with prtflux=yes.
h]h}(h]h]h]h]h]width600urifigs/NEWT/fig84.pngj*}j,jisuhjh jYh!h"hMubj.)}(h6Example of a flux plot image created with prtflux=yes.h]h/6Example of a flux plot image created with prtflux=yes.}(hjmh jkubah}(h]h]h]h]h]uhj-h!h"hMh jYubeh}(h](id244jXeh]h] fig9-2-84ah]h]jEcenteruhjhMh j͠hhh!h"j}j~jNsj}jXjNsubh)}(h
.. _9-2-5-15:h]h}(h]h]h]h]h]hid157uhh
hMh j͠hhh!h"ubeh}(h](postscript-graphics-filesj̠eh]h](postscript graphics files9-2-5-14eh]h]uhh#h jGhhh!h"hMgj}jj sj}j̠j subeh}(h](end-of-calculation-bannerj0eh]h](end-of-calculation banner9-2-5-13eh]h]uhh#h jhhh!h"hMTj}jj&sj}j0j&subh$)}(hhh](h))}(hMedia zone editsh]h/Media zone edits}(hjh jhhh!NhNubah}(h]h]h]h]h]uhh(h jhhh!h"hMubhM)}(hXNEWT automatically determines “zones” representing spatially independent
regions of the same media. For example, in a fuel pin cell, the fuel,
clad, and moderator are all considered separate zones. In an array of
such pin cells, each unique location is a unique zone. Zone numbers and
the geometric location of each zone are listed in the *Geometry
Specification*\ ” in :ref:`9-2-5-2-6`.h](h/XWNEWT automatically determines “zones” representing spatially independent
regions of the same media. For example, in a fuel pin cell, the fuel,
clad, and moderator are all considered separate zones. In an array of
such pin cells, each unique location is a unique zone. Zone numbers and
the geometric location of each zone are listed in the }(hXWNEWT automatically determines “zones” representing spatially independent
regions of the same media. For example, in a fuel pin cell, the fuel,
clad, and moderator are all considered separate zones. In an array of
such pin cells, each unique location is a unique zone. Zone numbers and
the geometric location of each zone are listed in the h jhhh!NhNubj)}(h*Geometry
Specification*h]h/Geometry
Specification}(hhh jubah}(h]h]h]h]h]uhjh jubh/ ” in }(h \ ” in h jhhh!NhNubj)}(h:ref:`9-2-5-2-6`h]j)}(hjԢh]h/ 9-2-5-2-6}(hhh j֢ubah}(h]h](jEstdstd-refeh]h]h]uhjh jҢubah}(h]h]h]h]h]refdochj refdomainjreftyperefrefexplicitrefwarnjW 9-2-5-2-6uhjh!h"hMh jubh/.}(hhh jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jhhubhM)}(hUpon completion of a calculation, NEWT provides an output edit of each
zone by number, giving the mixture number, average flux, fission power,
and volume, as shown in :numref:`fig9-2-85`.h](h/Upon completion of a calculation, NEWT provides an output edit of each
zone by number, giving the mixture number, average flux, fission power,
and volume, as shown in }(hUpon completion of a calculation, NEWT provides an output edit of each
zone by number, giving the mixture number, average flux, fission power,
and volume, as shown in h jhhh!NhNubj)}(h:numref:`fig9-2-85`h]jM)}(hjh]h/ fig9-2-85}(hhh j ubah}(h]h](jEstd
std-numrefeh]h]h]uhjLh jubah}(h]h]h]h]h]refdochj refdomainjreftypenumrefrefexplicitrefwarnjW fig9-2-85uhjh!h"hMh jubh/.}(hhh jhhh!NhNubeh}(h]h]h]h]h]uhhLh!h"hMh jhhubh)}(h.. _fig9-2-85:h]h}(h]h]h]h]h]h fig9-2-85uhh
hMh jhhh!h"ubj)}(hhh](j)}(hZ.. figure:: figs/NEWT/fig85.svg
:align: center
:width: 500
Media zone output edit.
h]h}(h]h]h]h]h]width500urifigs/NEWT/fig85.svgj*}j,jJsuhjh j:h!h"hMubj.)}(hMedia zone output edit.h]h/Media zone output edit.}(hjNh jLubah}(h]h]h]h]h]uhj-h!h"hMh j:ubeh}(h](id245j9eh]h] fig9-2-85ah]h]jEcenteruhjhMh jhhh!h"j}j_j/sj}j9j/subeh}(h](media-zone-editsjeh]h](media zone edits9-2-5-15eh]h]uhh#h jhhh!h"hMj}jkjsj}jjsubh$)}(hhh](h))}(hNotesh]h/Notes}(hjuh jshhh!NhNubah}(h]h]h]h]h]uhh(h jphhh!h"hMubh footnote)}(h-Formerly with Oak Ridge National Laboratory.
h](h label)}(h1h]h/1}(hhh jubah}(h]h]h]h]h]uhjh jubhM)}(h,Formerly with Oak Ridge National Laboratory.h]h/,Formerly with Oak Ridge National Laboratory.}(hjh jubah}(h]h]h]h]h]uhhLh!h"hMh jubeh}(h]hhah]h]1ah]h]hcahihjuhjh!h"hMh jphhhkKubhM)}(hhh](h j)}(hhh](j)}(hhh]h/alcouffe_review_1981}(hhh jubah}(h]h]h]h]h]support_smartquotesuhjh jubhM)}(hhh](h/R.}(hR.h jubh/ }(h h hM)}(hhh](h/Zhaopeng Zhong, Thomas}(hZhaopeng Zhong, Thomash jΣubh/ }(hjͣh jΣubh/J. Downar, Yunlin Xu, Mark}(hJ. Downar, Yunlin Xu, Markh jΣubjˣh/D. DeHart, and Kevin}(hD. DeHart, and Kevinh jΣubjˣh/
T. Clarno.}(h
T. Clarno.h jΣubh/ }(hj(h jΣubh/Implementation of two-level coarse-mesh finite difference acceleration in an arbitrary geometry, two-dimensional discrete ordinates transport method.}(hImplementation of two-level coarse-mesh finite difference acceleration in an arbitrary geometry, two-dimensional discrete ordinates transport method.h jΣubh/ }(hj(h jΣubj)}(hhh]h/Nuclear science and engineering}(hNuclear science and engineeringh jubah}(h]h]h]h]h]uhjh jΣubh/, 158(3):289–298, 2008.}(h, 158(3):289–298, 2008.h jΣubjh/Publisher: Taylor & Francis.}(hPublisher: Taylor & Francis.h jΣubeh}(h]h]h]h]h]uhhLh j)}(hhh](j)}(hhh]h/zhong_implementation_2008}(hhh jubah}(h]h]h]h]h]juhjh jubjΣeh}(h]zhong-implementation-2008ah]jah]zhong_implementation_2008ah]h]jahihjuhjh jhkKubububh/E. Alcouffe and E.}(hE. Alcouffe and E.h jubjˣh/
W. Larsen.}(h
W. Larsen.h jubjh/MReview of characteristic methods used to solve the linear transport equation.}(hMReview of characteristic methods used to solve the linear transport equation.h jubjh/=Technical Report, Los Alamos Scientific Lab., NM (USA), 1981.}(h=Technical Report, Los Alamos Scientific Lab., NM (USA), 1981.h jubeh}(h]h]h]h]h]uhhLh jubeh}(h]alcouffe-review-1981ah]jah]alcouffe_review_1981ah]h](jjP ehihjuhjh jhkKubj)}(hhh](j)}(hhh]h/alcouffe_computational_1979}(hhh jQubah}(h]h]h]h]h]juhjh jNubhM)}(hhh](h/R.}(hR.h j^ubjˣh/E. Alcouffe, E.}(hE. Alcouffe, E.h j^ubjˣh/
W. Larsen, W.}(h
W. Larsen, W.h j^ubjˣh/ F. Miller}(h F. Millerh j^ubjˣh/
Jr, and B.}(h
Jr, and B.h j^ubjˣh/
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id_countercollectionsCounter}jKsRparse_messages](j7)}(hhh]hM)}(h;Enumerated list start value not ordinal-1: "M" (ordinal 13)h]h/?Enumerated list start value not ordinal-1: “M” (ordinal 13)}(hhh j ubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypeINFOsourceh"lineKuhj6h h%hhh!h"hKubj7)}(hhh]hM)}(h:Enumerated list start value not ordinal-1: "2" (ordinal 2)h]h/>Enumerated list start value not ordinal-1: “2” (ordinal 2)}(hhh j%ubah}(h]h]h]h]h]uhhLh j"ubah}(h]h]h]h]h]levelKtypejsourceh"lineKuhj6h jhhh!h"hKubj7)}(hhh]hM)}(h:Enumerated list start value not ordinal-1: "3" (ordinal 3)h]h/>Enumerated list start value not ordinal-1: “3” (ordinal 3)}(hhh j@ubah}(h]h]h]h]h]uhhLh j=ubah}(h]h]h]h]h]levelKtypejsourceh"lineKuhj6h jhhh!h"hMubj8jTjojjjj7)}(hhh]hM)}(hADuplicate implicit target name: "assembly discontinuity factors".h]h/EDuplicate implicit target name: “assembly discontinuity factors”.}(hhh j[ubah}(h]h]h]h]h]uhhLh jXubah}(h]h]h]h]h]jalevelKtypejsourceh"lineMBuhj6h j1~hhh!h"hMBubj7)}(hhh]hM)}(h2Duplicate implicit target name: "control options".h]h/6Duplicate implicit target name: “control options”.}(hhh jvubah}(h]h]h]h]h]uhhLh jsubah}(h]h]h]h]h]j_alevelKtypejsourceh"lineMuhj6h jhhh!h"hMubj7)}(hhh]hM)}(h2Duplicate implicit target name: "pin-power edits".h]h/6Duplicate implicit target name: “pin-power edits”.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]j$alevelKtypejsourceh"lineMuhj6h jUhhh!h"hMubj7)}(hhh]hM)}(hADuplicate implicit target name: "assembly discontinuity factors".h]h/EDuplicate implicit target name: “assembly discontinuity factors”.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]j՞alevelKtypejsourceh"lineMuhj6h jMhhh!h"hMubetransform_messages](j7)}(hhh]hM)}(hhh]h/)Hyperlink target "id1" is not referenced.}(hhh jɭubah}(h]h]h]h]h]uhhLh jƭubah}(h]h]h]h]h]levelKtypejsourceh"lineKuhj6ubj7)}(hhh]hM)}(hhh]h/)Hyperlink target "id3" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineK:uhj6ubj7)}(hhh]hM)}(hhh]h/)Hyperlink target "id6" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineKMuhj6ubj7)}(hhh]hM)}(hhh]h/)Hyperlink target "id7" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineKiuhj6ubj7)}(hhh]hM)}(hhh]h/)Hyperlink target "id8" is not referenced.}(hhh j1ubah}(h]h]h]h]h]uhhLh j.ubah}(h]h]h]h]h]levelKtypejsourceh"lineKuhj6ubj7)}(hhh]hM)}(hhh]h/)Hyperlink target "id9" is not referenced.}(hhh jKubah}(h]h]h]h]h]uhhLh jHubah}(h]h]h]h]h]levelKtypejsourceh"lineKuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id10" is not referenced.}(hhh jeubah}(h]h]h]h]h]uhhLh jbubah}(h]h]h]h]h]levelKtypejsourceh"lineKuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id11" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh j|ubah}(h]h]h]h]h]levelKtypejsourceh"lineKuhj6ubj7)}(hhh]hM)}(hhh]h/6Hyperlink target "equation-eq9-2-1" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/6Hyperlink target "equation-eq9-2-2" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/6Hyperlink target "equation-eq9-2-3" is not referenced.}(hhh jˮubah}(h]h]h]h]h]uhhLh jȮubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id13" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/6Hyperlink target "equation-eq9-2-4" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/6Hyperlink target "equation-eq9-2-5" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/6Hyperlink target "equation-eq9-2-6" is not referenced.}(hhh j0ubah}(h]h]h]h]h]uhhLh j-ubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/6Hyperlink target "equation-eq9-2-7" is not referenced.}(hhh jIubah}(h]h]h]h]h]uhhLh jFubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/.Hyperlink target "fig9-2-1" is not referenced.}(hhh jbubah}(h]h]h]h]h]uhhLh j_ubah}(h]h]h]h]h]levelKtypejsourceh"lineMruhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id23" is not referenced.}(hhh j|ubah}(h]h]h]h]h]uhhLh jyubah}(h]h]h]h]h]levelKtypejsourceh"lineMyuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id25" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/6Hyperlink target "equation-eq9-2-8" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/6Hyperlink target "equation-eq9-2-9" is not referenced.}(hhh jɯubah}(h]h]h]h]h]uhhLh jƯubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-10" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh j߯ubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-11" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-12" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/.Hyperlink target "fig9-2-2" is not referenced.}(hhh j-ubah}(h]h]h]h]h]uhhLh j*ubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id26" is not referenced.}(hhh jGubah}(h]h]h]h]h]uhhLh jDubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id27" is not referenced.}(hhh jaubah}(h]h]h]h]h]uhhLh j^ubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id28" is not referenced.}(hhh j{ubah}(h]h]h]h]h]uhhLh jxubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/.Hyperlink target "fig9-2-3" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineM:uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-13" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-14" is not referenced.}(hhh jȰubah}(h]h]h]h]h]uhhLh jŰubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-15" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jްubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-16" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-17" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-18" is not referenced.}(hhh j,ubah}(h]h]h]h]h]uhhLh j)ubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-19" is not referenced.}(hhh jEubah}(h]h]h]h]h]uhhLh jBubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-20" is not referenced.}(hhh j^ubah}(h]h]h]h]h]uhhLh j[ubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/.Hyperlink target "fig9-2-4" is not referenced.}(hhh jwubah}(h]h]h]h]h]uhhLh jtubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id29" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-21" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/.Hyperlink target "fig9-2-5" is not referenced.}(hhh jıubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id35" is not referenced.}(hhh jޱubah}(h]h]h]h]h]uhhLh j۱ubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-22" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-23" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-24" is not referenced.}(hhh j*ubah}(h]h]h]h]h]uhhLh j'ubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-25" is not referenced.}(hhh jCubah}(h]h]h]h]h]uhhLh j@ubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id36" is not referenced.}(hhh j\ubah}(h]h]h]h]h]uhhLh jYubah}(h]h]h]h]h]levelKtypejsourceh"lineM#uhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id38" is not referenced.}(hhh jvubah}(h]h]h]h]h]uhhLh jsubah}(h]h]h]h]h]levelKtypejsourceh"lineMXuhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-26" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-27" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/.Hyperlink target "fig9-2-6" is not referenced.}(hhh j²ubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id39" is not referenced.}(hhh jܲubah}(h]h]h]h]h]uhhLh jٲubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id40" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id41" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh j
ubah}(h]h]h]h]h]levelKtypejsourceh"lineM3uhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id42" is not referenced.}(hhh j*ubah}(h]h]h]h]h]uhhLh j'ubah}(h]h]h]h]h]levelKtypejsourceh"lineMJuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id51" is not referenced.}(hhh jDubah}(h]h]h]h]h]uhhLh jAubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id52" is not referenced.}(hhh j^ubah}(h]h]h]h]h]uhhLh j[ubah}(h]h]h]h]h]levelKtypejsourceh"lineM+uhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id55" is not referenced.}(hhh jxubah}(h]h]h]h]h]uhhLh juubah}(h]h]h]h]h]levelKtypejsourceh"lineMLuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id58" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id59" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id60" is not referenced.}(hhh jƳubah}(h]h]h]h]h]uhhLh jóubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id62" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jݳubah}(h]h]h]h]h]levelKtypejsourceh"lineM:uhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id63" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMtuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id64" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id65" is not referenced.}(hhh j.ubah}(h]h]h]h]h]uhhLh j+ubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/.Hyperlink target "fig9-2-7" is not referenced.}(hhh jHubah}(h]h]h]h]h]uhhLh jEubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/.Hyperlink target "fig9-2-8" is not referenced.}(hhh jbubah}(h]h]h]h]h]uhhLh j_ubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id66" is not referenced.}(hhh j|ubah}(h]h]h]h]h]uhhLh jyubah}(h]h]h]h]h]levelKtypejsourceh"lineMTuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id67" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMbuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id68" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id69" is not referenced.}(hhh jʴubah}(h]h]h]h]h]uhhLh jǴubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id70" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/.Hyperlink target "fig9-2-9" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-10" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id71" is not referenced.}(hhh j2ubah}(h]h]h]h]h]uhhLh j/ubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-11" is not referenced.}(hhh jLubah}(h]h]h]h]h]uhhLh jIubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id72" is not referenced.}(hhh jfubah}(h]h]h]h]h]uhhLh jcubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id73" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh j}ubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-12" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id74" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id75" is not referenced.}(hhh jεubah}(h]h]h]h]h]uhhLh j˵ubah}(h]h]h]h]h]levelKtypejsourceh"lineM0uhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-13" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMYuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id76" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineM`uhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-14" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id77" is not referenced.}(hhh j6ubah}(h]h]h]h]h]uhhLh j3ubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-15" is not referenced.}(hhh jPubah}(h]h]h]h]h]uhhLh jMubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-16" is not referenced.}(hhh jjubah}(h]h]h]h]h]uhhLh jgubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-17" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-18" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id78" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id79" is not referenced.}(hhh jҶubah}(h]h]h]h]h]uhhLh j϶ubah}(h]h]h]h]h]levelKtypejsourceh"lineM uhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-19" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineM+ uhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id80" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineM2 uhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-20" is not referenced.}(hhh j ubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineM uhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id81" is not referenced.}(hhh j:ubah}(h]h]h]h]h]uhhLh j7ubah}(h]h]h]h]h]levelKtypejsourceh"lineM uhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-21" is not referenced.}(hhh jTubah}(h]h]h]h]h]uhhLh jQubah}(h]h]h]h]h]levelKtypejsourceh"lineM uhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-22" is not referenced.}(hhh jnubah}(h]h]h]h]h]uhhLh jkubah}(h]h]h]h]h]levelKtypejsourceh"lineM uhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id82" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineM uhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-23" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMt
uhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id83" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineM
uhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-24" is not referenced.}(hhh jַubah}(h]h]h]h]h]uhhLh jӷubah}(h]h]h]h]h]levelKtypejsourceh"lineM
uhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-25" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineM
uhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-26" is not referenced.}(hhh j
ubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineM
uhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-27" is not referenced.}(hhh j$ubah}(h]h]h]h]h]uhhLh j!ubah}(h]h]h]h]h]levelKtypejsourceh"lineM
uhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-28" is not referenced.}(hhh j>ubah}(h]h]h]h]h]uhhLh j;ubah}(h]h]h]h]h]levelKtypejsourceh"lineM
uhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id84" is not referenced.}(hhh jXubah}(h]h]h]h]h]uhhLh jUubah}(h]h]h]h]h]levelKtypejsourceh"lineM
uhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id85" is not referenced.}(hhh jrubah}(h]h]h]h]h]uhhLh joubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-29" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id86" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-30" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineM%uhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id87" is not referenced.}(hhh jڸubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineM,uhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-31" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineM:uhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id88" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineM|uhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id89" is not referenced.}(hhh j(ubah}(h]h]h]h]h]uhhLh j%ubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id90" is not referenced.}(hhh jBubah}(h]h]h]h]h]uhhLh j?ubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id91" is not referenced.}(hhh j\ubah}(h]h]h]h]h]uhhLh jYubah}(h]h]h]h]h]levelKtypejsourceh"lineM uhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-32" is not referenced.}(hhh jvubah}(h]h]h]h]h]uhhLh jsubah}(h]h]h]h]h]levelKtypejsourceh"lineM8uhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id92" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMSuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id93" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineM^uhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-33" is not referenced.}(hhh jĹubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMquhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id94" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh j۹ubah}(h]h]h]h]h]levelKtypejsourceh"lineMxuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-34" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id95" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-35" is not referenced.}(hhh j,ubah}(h]h]h]h]h]uhhLh j)ubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id96" is not referenced.}(hhh jFubah}(h]h]h]h]h]uhhLh jCubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-36" is not referenced.}(hhh j`ubah}(h]h]h]h]h]uhhLh j]ubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id97" is not referenced.}(hhh jzubah}(h]h]h]h]h]uhhLh jwubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/.Hyperlink target "tab9-2-1" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id98" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-28" is not referenced.}(hhh jȺubah}(h]h]h]h]h]uhhLh jźubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-29" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/*Hyperlink target "id99" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineM+
uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-30" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-31" is not referenced.}(hhh j-ubah}(h]h]h]h]h]uhhLh j*ubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-32" is not referenced.}(hhh jFubah}(h]h]h]h]h]uhhLh jCubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id100" is not referenced.}(hhh j_ubah}(h]h]h]h]h]uhhLh j\ubah}(h]h]h]h]h]levelKtypejsourceh"lineMN
uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-33" is not referenced.}(hhh jyubah}(h]h]h]h]h]uhhLh jvubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(3ahhh]hM)}(hhh]h/+Hyperlink target "id101" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineM]
uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-34" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-35" is not referenced.}(hhh jŻubah}(h]h]h]h]h]uhhLh j»ubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id102" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jۻubah}(h]h]h]h]h]levelKtypejsourceh"lineMq
uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-36" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id103" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineM
uhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id104" is not referenced.}(hhh j+ubah}(h]h]h]h]h]uhhLh j(ubah}(h]h]h]h]h]levelKtypejsourceh"lineM
uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-37" is not referenced.}(hhh jEubah}(h]h]h]h]h]uhhLh jBubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-38" is not referenced.}(hhh j^ubah}(h]h]h]h]h]uhhLh j[ubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-39" is not referenced.}(hhh jwubah}(h]h]h]h]h]uhhLh jtubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id105" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineM
uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-40" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/7Hyperlink target "equation-eq9-2-41" is not referenced.}(hhh jüubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"uhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id106" is not referenced.}(hhh jܼubah}(h]h]h]h]h]uhhLh jټubah}(h]h]h]h]h]levelKtypejsourceh"lineM
uhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id107" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/.Hyperlink target "tab9-2-2" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh j
ubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-37" is not referenced.}(hhh j*ubah}(h]h]h]h]h]uhhLh j'ubah}(h]h]h]h]h]levelKtypejsourceh"lineMBuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-38" is not referenced.}(hhh jDubah}(h]h]h]h]h]uhhLh jAubah}(h]h]h]h]h]levelKtypejsourceh"lineMIuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-39" is not referenced.}(hhh j^ubah}(h]h]h]h]h]uhhLh j[ubah}(h]h]h]h]h]levelKtypejsourceh"lineMPuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-40" is not referenced.}(hhh jxubah}(h]h]h]h]h]uhhLh juubah}(h]h]h]h]h]levelKtypejsourceh"lineMWuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id108" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMhuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id109" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id110" is not referenced.}(hhh jƽubah}(h]h]h]h]h]uhhLh jýubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-41" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jݽubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id111" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id112" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineM?uhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-42" is not referenced.}(hhh j.ubah}(h]h]h]h]h]uhhLh j+ubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-43" is not referenced.}(hhh jHubah}(h]h]h]h]h]uhhLh jEubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id114" is not referenced.}(hhh jbubah}(h]h]h]h]h]uhhLh j_ubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id115" is not referenced.}(hhh j|ubah}(h]h]h]h]h]uhhLh jyubah}(h]h]h]h]h]levelKtypejsourceh"lineMVuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id116" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id117" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-44" is not referenced.}(hhh jʾubah}(h]h]h]h]h]uhhLh jǾubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-45" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id118" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-46" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-47" is not referenced.}(hhh j2ubah}(h]h]h]h]h]uhhLh j/ubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id119" is not referenced.}(hhh jLubah}(h]h]h]h]h]uhhLh jIubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-48" is not referenced.}(hhh jfubah}(h]h]h]h]h]uhhLh jcubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-49" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh j}ubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id120" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-50" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMauhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-51" is not referenced.}(hhh jοubah}(h]h]h]h]h]uhhLh j˿ubah}(h]h]h]h]h]levelKtypejsourceh"lineMiuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-52" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMpuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id121" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMwuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-53" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-54" is not referenced.}(hhh j6ubah}(h]h]h]h]h]uhhLh j3ubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id122" is not referenced.}(hhh jPubah}(h]h]h]h]h]uhhLh jMubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id123" is not referenced.}(hhh jjubah}(h]h]h]h]h]uhhLh jgubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-55" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id124" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id125" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-56" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id127" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-57" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id128" is not referenced.}(hhh j ubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-58" is not referenced.}(hhh j:ubah}(h]h]h]h]h]uhhLh j7ubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id129" is not referenced.}(hhh jTubah}(h]h]h]h]h]uhhLh jQubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-59" is not referenced.}(hhh jnubah}(h]h]h]h]h]uhhLh jkubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id130" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-60" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id131" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-61" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineM*uhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id132" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineM1uhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-62" is not referenced.}(hhh j
ubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineM:uhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id133" is not referenced.}(hhh j$ubah}(h]h]h]h]h]uhhLh j!ubah}(h]h]h]h]h]levelKtypejsourceh"lineMAuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-63" is not referenced.}(hhh j>ubah}(h]h]h]h]h]uhhLh j;ubah}(h]h]h]h]h]levelKtypejsourceh"lineMJuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id134" is not referenced.}(hhh jXubah}(h]h]h]h]h]uhhLh jUubah}(h]h]h]h]h]levelKtypejsourceh"lineMQuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-64" is not referenced.}(hhh jrubah}(h]h]h]h]h]uhhLh joubah}(h]h]h]h]h]levelKtypejsourceh"lineM\uhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id135" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMcuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-65" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMpuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id136" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMwuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-66" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id137" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-67" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id138" is not referenced.}(hhh j(ubah}(h]h]h]h]h]uhhLh j%ubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-68" is not referenced.}(hhh jBubah}(h]h]h]h]h]uhhLh j?ubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id139" is not referenced.}(hhh j\ubah}(h]h]h]h]h]uhhLh jYubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-69" is not referenced.}(hhh jvubah}(h]h]h]h]h]uhhLh jsubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id140" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-70" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id141" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-71" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineM!uhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-72" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineM)uhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id142" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineM0uhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-73" is not referenced.}(hhh j,ubah}(h]h]h]h]h]uhhLh j)ubah}(h]h]h]h]h]levelKtypejsourceh"lineM:uhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id143" is not referenced.}(hhh jFubah}(h]h]h]h]h]uhhLh jCubah}(h]h]h]h]h]levelKtypejsourceh"lineMAuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-74" is not referenced.}(hhh j`ubah}(h]h]h]h]h]uhhLh j]ubah}(h]h]h]h]h]levelKtypejsourceh"lineMxuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id144" is not referenced.}(hhh jzubah}(h]h]h]h]h]uhhLh jwubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-75" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id145" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-76" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id147" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id148" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-77" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id149" is not referenced.}(hhh j0ubah}(h]h]h]h]h]uhhLh j-ubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-78" is not referenced.}(hhh jJubah}(h]h]h]h]h]uhhLh jGubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id150" is not referenced.}(hhh jdubah}(h]h]h]h]h]uhhLh jaubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-79" is not referenced.}(hhh j~ubah}(h]h]h]h]h]uhhLh j{ubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id151" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-80" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id153" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-81" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineM'uhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id154" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineM.uhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-82" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMJuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id155" is not referenced.}(hhh j4ubah}(h]h]h]h]h]uhhLh j1ubah}(h]h]h]h]h]levelKtypejsourceh"lineMQuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-83" is not referenced.}(hhh jNubah}(h]h]h]h]h]uhhLh jKubah}(h]h]h]h]h]levelKtypejsourceh"lineM]uhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id156" is not referenced.}(hhh jhubah}(h]h]h]h]h]uhhLh jeubah}(h]h]h]h]h]levelKtypejsourceh"lineMduhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-84" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h/+Hyperlink target "id157" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubj7)}(hhh]hM)}(hhh]h//Hyperlink target "fig9-2-85" is not referenced.}(hhh jubah}(h]h]h]h]h]uhhLh jubah}(h]h]h]h]h]levelKtypejsourceh"lineMuhj6ubetransformerN
decorationNhhub.