DEVC.rst.txt 34.5 KB
Newer Older
 Batson Iii committed Nov 17, 2020 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 .. _DEVC: DEVC: Denovo EigenValue Calculation =================================== *Douglas E. Peplow and Cihangir Celik* Introduction ------------ The DEVC (Denovo EigenValue Calculation) sequence is an interface to the Denovo discrete-ordinates package :cite:evans_denovo_2010 for calculating criticality eigenvalue problems. This sequence reads an input file very similar to a CSAS6 input file :cite:goluoglu_monte_2011 that contains an extra block of input for describing the Denovo mesh grid and calculational parameters. Many of the subroutines are shared from the MAVRIC routines that interface with Denovo for fixed-source calculations. This manual assumes that the user is familiar with the discrete-ordinates method for radiation transport and the Denovo package. DEVC provides an easy way for users to modify existing CSAS6 inputs and use them to run Denovo. The DEVC sequence also provides a way to create mesh geometry for Denovo from the combinatorial solid geometry description used by KENO-VI. The steps in the DEVC sequence are listed in :numref:tab2-4a-1. .. _tab2-4a-1: .. table:: Steps in DEVC for an input file named *input*.inp :align: center +-----------------+-----------------+-----------------+-----------------+ | Step | Module/Task | Creates file | To stop after | +=================+=================+=================+=================+ | 0 | Check user | | | | | input | | | +-----------------+-----------------+-----------------+-----------------+ | | | | | +-----------------+-----------------+-----------------+-----------------+ | 1 | Self-shielding | | | | | (celldata/cellm | | | | | ix) | | | | | calculations | | | +-----------------+-----------------+-----------------+-----------------+ | | | | | +-----------------+-----------------+-----------------+-----------------+ | 2 | Produces | | | | | optional \*.png | | | | | plots | | | +-----------------+-----------------+-----------------+-----------------+ | | Produces | | parm=check | | | optional | | | | | \*.3mdap files | | | | | (to visualize | | | | | grid in | | | | | MeshFileViewer) | | | +-----------------+-----------------+-----------------+-----------------+ | | | | | +-----------------+-----------------+-----------------+-----------------+ | 3 | Creates AMPX | ft02f001 | parm=cross | | | cross sections | | | | | for the “real” | | | | | materials | | | +-----------------+-----------------+-----------------+-----------------+ | | | | | +-----------------+-----------------+-----------------+-----------------+ | 4 | Creates Denovo | xkba_b.inp | parm=input | | | binary stream | | | | | input file and | input.mmt | | | | the | | | | | | | | | | macromaterial | | | | | table file | | | +-----------------+-----------------+-----------------+-----------------+ | | | | | +-----------------+-----------------+-----------------+-----------------+ | 5 | Runs Denovo to | input.dff or| | | | compute | | | | | :math:k_{ | input.dso | | | | \text{eff}} | | | | | and | | | | | either the | | | | | fluxes or the | | | | | fission source | | | +-----------------+-----------------+-----------------+-----------------+ The DEVC sequence uses KENO-VI geometry. Users can specify what output Denovo will generate: fluxes by space and energy in a binary \*.dff (Denovo flux file) file or the space-only fission source distribution in a binary \*.dso (Denovo spatial output) file. The eigenvalue is printed in the main output text file. Some of the more common KENO starting source types are supported. Other starting source types may be added or extended to all of the different array types in the future. Currently, starting sources are not sent to Denovo because the Arnoldi solver does not use it. This may change in the future. Sequence input -------------- The input file for a DEVC calculation looks similar to a CSAS6 input file, as shown in :numref:tab2-4a-2. The major difference is that the parameter block contains information for the Denovo calculation, not the KENO Monte Carlo calculation. A macromaterial block is used to describe how the KENO-VI materials are mapped onto the Denovo mesh grid. Only multi-group cross-section libraries can be used with Denovo. .. list-table:: Input file for a DEVC calculation (and differences with a CSAS6 input file, where black text is the same as CSAS6 and green text is new for DEVC sequence) :name: tab2-4a-2 :align: center * - .. image:: figs/DEVC/tab2.png Parameters block ~~~~~~~~~~~~~~~~ This block contains the parameters for the Denovo eigenvalue calculation, the grid geometry, and the macromaterials. Boundary conditions listed in the parameters block will override those listed in the bounds block (using CSAS6 syntax). :numref:tab2-4a-3 lists the Denovo calculation parameters and their default values, and :numref:tab2-4a-4 lists the keywords for the setting the boundary conditions and file saving options. The grid geometry is defined in a sub-block in the parameters block, or the keyword “gridGeometryID=\ *n*\ ” can be used to point to a grid geometry defined in its own input block. .. list-table:: Denovo parameters in the parameters block :align: center :name: tab2-4a-3 * - .. image:: figs/DEVC/tab3.png .. list-table:: Boundary conditions and what type of file to save :align: center :name: tab2-4a-4 * - .. image:: figs/DEVC/tab4.png Grid geometry block ~~~~~~~~~~~~~~~~~~~ Grid geometries (“gridGeometry *id*\ ”) require an identification number and then a description of a three-dimensional rectangular mesh by specifying the bounding planes of the cells in each of the *x*, *y*, and *z* dimensions. The keyword “xPlanes … end” can be used to list plane values (in any order). The keyword “xLinear *n* *a* *b*\ ” can be used to specify *n* cells between *a* and *b*. The keywords “xPlanes” and “xLinear” can be used together and multiple times – they will simply add planes to any already defined for that dimension. Any duplicate planes will be removed. Similar keywords are used for the *y* and *z* dimensions. When using multiple instances of the keywords \*Linear and \*Planes for a given dimension, duplicates should be removed from the final list. In some cases, double precision math will leave two planes that are nearly identical but not removed (e.g., 6.0 and 5.9999999). To prevent this, a default tolerance is set to remove planes that are within 10\ :sup:-6 cm of each other. The user is free to change this by using the keyword “tolerance=” and specifying something else. Note that the tolerance can be reset to a different value in between each use of \*Linear or \*Planes. The keyword “make3dmap” for a particular grid geometry definition will create a file called “\ *outputName*.grid\ *id*.3dmap”, which can be visualized using the Java Mesh File Viewer. These files will contain crude geometry information (unit, region, material) that corresponds to the center of each voxel. Keywords for the grid geometry block are listed in :numref:tab2-4a-5. .. list-table:: Grid geometry input keywords :align: center :name: tab2-4a-5 * - .. image:: figs/DEVC/tab5.png Macromaterial block ~~~~~~~~~~~~~~~~~~~ In order to get more accurate solutions from a coarse-mesh discrete-ordinates calculation, Denovo can represent the material in each voxel of the mesh as a volume-weighted mixture of the real materials in the problem. When constructing the Denovo input, DEVC can estimate the volume fraction taken by each real material in each voxel by a sampling method. The user can specify parameters for how to sample the geometry. Note that finer sampling makes more accurate estimates of the material fraction but requires more setup time to create the Denovo input. Users should understand how the macromaterials are sampled and consider that when constructing a mesh grid. This is especially important for geometries that contain arrays. Careful consideration should be given when overlaying a mesh on a geometry that contains arrays of arrays. Because the list of macromaterials could become large, the user can also specify a tolerance for how close two different macromaterials can be to be considered the same, thereby reducing the total number of macromaterials. The macromaterial tolerance, “mmTolerance=”, is used for creating a different macromaterial from the ones already created by looking at the infinity norm between two macromaterials. The number of macromaterials does not appreciably impact Denovo run time or memory requirements. Keywords for the macromaterial block are listed :numref:tab2-4a-6. Two different sampling methods are available – ray tracing :cite:ibrahim_improving_2009 with the keyword mmRayTest and point testing :cite:johnson_fast_2013 with the keyword mmPointTest. .. list-table:: Macromaterial block input :align: center :name: tab2-4a-6 * - .. image:: figs/DEVC/tab6.png Ray tracing ^^^^^^^^^^^ This method estimates the volume of different materials in the Denovo mesh grid elements by throwing rays through the KENO-VI geometry and computing the average track lengths through the each material. Rays are traced in all three dimensions to better estimate the volume fractions of materials within each voxel. The mmSubCell parameter controls how many rays to trace in each voxel in each dimension. For example, if mmSubCell=\ :math:\text{\ n}, then when tracing rays in the *z* dimension, each column of voxels uses a set of :math:n \times n rays starting uniformly spaced in the *x* and *y* dimensions. With rays being cast from all three orthogonal directions, then a total of :math:3n^{2} rays are used to sample each voxel. One can think of subcells as an equally spaced sub-mesh with a single ray positioned at each center. The number of subcells in each direction, and hence the number of rays, can be explicitly given with mmSubCells ny nz nx nz nx ny end keyword for rays parallel to the :math:x axis, :math:y axis, and :math:z axis. :numref:fig2-4a-1 shows different subcell configurations (in two dimensions) for a given voxel. .. _fig2-4a-1: .. figure:: figs/DEVC/fig1.png :align: center :width: 500 Ray positions within a voxel with different mmSubCells parameters. Ray tracing is a more robust method compared to the simple point testing method used in previous versions of SCALE/MAVRIC; however, it requires more memory than point testing. Ray tracing gives more accurate estimates of volume fractions because track lengths across a voxel give more information than a series of test points. Ray tracing is also much faster than point testing because the particle tracking routines are optimized for quickly determining lists of materials and distance along a given ray. Ray tracing operates on the grid geometry supplied by the user and shoots rays in all three directions starting from the lower bounds of the mesh grid. An example of arbitrary assembly geometry is shown in :numref:fig2-4a-2. A ray consists of a number of steps that corresponds to crossing a different material along the path of the ray. Ratios of each step’s length to the voxel length in the ray’s direction determine the material volume fraction of that step in that voxel, and summation of the same material volume fractions gives the material volume fraction of that material in that voxel. Ray tracing through a single voxel that contains a fuel pin is illustrated in :numref:fig2-4a-3. .. _fig2-4a-2: .. figure:: figs/DEVC/fig2.png :align: center :width: 600 Geometry model (left) and the Denovo representation (right) of an assembly using macromaterials determined by ray tracing. The final constructed macromaterials for this model are also shown in :numref:fig2-4a-2. Voxels that contain only a single material are assigned that original material number in the constructed macromaterials. For the voxels that contain a fuel pin with three different materials, the result is a new macromaterial consisting of the volume weighted fractions of each original material. After the rays are shot in all three directions, the material volume fractions are updated and macromaterials are created by using these material volume fractions. Material volume fraction calculations for a single voxel, as shown in :numref:fig2-4a-3, are given by .. math:: F_{m} = \ \sum_{d = x,y,z}^{}{\sum_{r = 1}^{N_{r}}{\sum_{s = 1}^{N_{s}}\left\{ \begin{matrix} \frac{L_{d,r,s}}{L_{d}},\ \ \ & m_{s} = = m \\ 0,\ \ \ & \mathrm{\text{otherwise}} \\ \end{matrix} \right.\ }} \ \ \ \ \ \ \mathrm{\text{ and }} \ \ \ \ \ \ \ V_{m} = \frac{F_{m}}{\sum_{n = 1}^{N_{m}}F_{n}}\ , where *F*\ :sub:m = sampled fraction of material *m* in the voxel, *d* = direction of the rays (*x*, *y*, *z*), *r* = ray number, *N*\ :sub:r = total number of rays in the voxel for direction of *d,* *s* = step number, *N*\ :sub:s = total number of steps for ray *r* in the voxel for direction of *d,* *L*\ :sub:d,r,s = length of the steps *s* for ray *r* in the voxel for direction of *d,* *L*\ :sub:d, = length of the voxel along direction of *d,* *m*\ :sub:s = material of step *s,* *m* = material number, *N*\ :sub:m = total number of materials in the voxel, and *V*\ :sub:m = volume fraction of material *m* in the voxel. .. _fig2-4a-3: .. figure:: figs/DEVC/fig3.png :align: center :width: 400 Ray tracing (in two dimensions) through a voxel. Point testing ^^^^^^^^^^^^^ The recursive bisection method uses a series of point tests to determine the macromaterial fractions. For a given voxel, the material at the center is compared to the material at the eight corners. If they are all the same, the entire volume is considered to be made of that material. If different, the volume is divided into two in each dimension. Each subvolume is tested, and the method is then applied to the subvolumes that are not of a single material. When the ratio of the volume of the tested region to the original voxel becomes less than a user-specified tolerance (in the range of 10\ :sup:-1 to 10\ :sup:-4), then further subdivision and testing are stopped. This is illustrated in :numref:fig2-4a-4. .. _fig2-4a-4: .. figure:: figs/DEVC/fig4.png :align: center :width: 600 Progression of the recursive bisection method (from upper left to lower right). In point testing, the keyword “mmTolerance=\ *f*\ ” is interpreted to be where *f* is the smallest fraction of the voxel volume to consider. This same tolerance *f* is also used to limit the number of macromaterials. Before a new macromaterial is created, if one already exists where the fraction of each actual material matches to within the given tolerance, then the existing material will be used. If using only a single point at the center of each voxel, use “mmTolerance=1”. The mmSubCell keyword is not used in point testing. Example ^^^^^^^ :numref:fig2-4a-5 shows an example of a cask geometry with two types of spent fuel (yellows), steel (blue), resin (green), and other metals (gray). When the Denovo geometry is set up by testing only the center of each mesh cell, the curved surfaces are not well represented (upper right). By applying the ray-tracing method and defining a new material made of partial fractions of the original materials, an improved Denovo model can be made. In the lower left of the figure, the Denovo model was constructed using one ray (in each dimension) per voxel and a tolerance of 0.1. This gives 20 new materials that are a mixture of the original 13 actual materials and void. With mmSubCells=3 and an mmTolerance=0.01, 139 macromaterials are created. A macromaterial table listing the fractions of each macromaterial is saved to a file called “\ *outputName*.mmt”, where *outputName* is the name the user chose for his or her output file. This file can be used by the Mesh File Viewer to display the macromaterials as mixtures of the actual materials, as seen in lower row of :numref:fig2-4a-5. See the Mesh File Viewer help pages for more information on how to use colormap files and macromaterial tables. .. _fig2-4a-5: .. figure:: figs/DEVC/fig5.png :align: center :width: 600 Cask geometry model (upper left) and the Denovo representation using (upper right) cell center testing. Representations using macromaterials determined by ray tracing are shown for (lower left) mmSubCell=1/mmTolerance=0.1 and (lower right) mmSubCell=3/mmTolerance=0.01. Starting sources block ~~~~~~~~~~~~~~~~~~~~~~ The default KENO-VI starting source is “flat over the volume specified by the unrotated, untranslated geometry record specified in the first position of the global unit boundary record in fissile material only”. For DEVC, the default starting source strength is uniform in the fissile voxels contained within the bounding box of the global unit (uniform density). If macromaterials are used, the amounts in each voxel are volume averaged between fissile and non-fissile materials. :numref:tab2-4a-7 and :numref:tab2-4a-8 describe the starting sources available in the DEVC interface to Denovo. .. _tab2-4a-7: .. table:: Starting source types (within the fissile areas of the listed shape) :align: center +-----------------------+-----------------------+-----------------------+ | | KENO-VI start type | DEVC | +=======================+=======================+=======================+ | nst=0 | the first surface of | The bounding box of | | | boundary (default) | global unit | +-----------------------+-----------------------+-----------------------+ | nst=0 | Within boundary of | Not supported | | | global array having a | | | | reflector key set to | | | | false | | +-----------------------+-----------------------+-----------------------+ | nst=0 | A cuboid defined by | Supported | | | XSM, XSP, YSM, YSP, | | | | ZSM, and ZSP | | +-----------------------+-----------------------+-----------------------+ | nst=1 | A cuboid defined by | Supported | | | XSM, XSP, YSM, YSP, | | | | ZSM, and ZSP with | | | | cosine distributions | | +-----------------------+-----------------------+-----------------------+ | nst=2 | Arbitrary fraction | Supported for some | | | (FCT) in element NXS, | array types (see | | | NYS, NZS of the | :numref:tab2-4a-8) | | | global array with the | | | | remainder in a cuboid | | | | defined by XSM, XSP, | | | | YSM, YSP, ZSM, and | | | | ZSP with cosine | | | | distributions | | +-----------------------+-----------------------+-----------------------+ | nst=3 | At the location TFX, | Supported for some | | | TFY, TFZ in the | array types (see | | | element NXS, NYS, NZS | :numref:tab2-4a-8) | | | of the global array | | +-----------------------+-----------------------+-----------------------+ | nst=4 | At the location TFX, | Supported | | | TFY, TFZ in units NBX | | | | of the global array | | +-----------------------+-----------------------+-----------------------+ | nst=5 | Across units NBX in | Not supported | | | the global array | | +-----------------------+-----------------------+-----------------------+ | nst=6 | List of points TFX, | Limited to 1 point | | | TFY, TFZ in global | | | | coordinates | | +-----------------------+-----------------------+-----------------------+ | nst=6 | List of points TFX, | Limited to 1 point | | | TFY, TFZ in element | and only for some | | | NXS, NYS, NZS of the | array types (see | | | global array | :numref:tab2-4a-8) | +-----------------------+-----------------------+-----------------------+ | nst=7 | Flat distributions in | Supported | | | X and Y with | | | | [1-cos\ :sup:2\ (z)]| | | | in Z for a cuboid | | | | defined by XSM, XSP, | | | | YSM, YSP, ZSM, and | | | | ZSP | | +-----------------------+-----------------------+-----------------------+ | nst=8 | Flat distributions in | Not supported | | | X and Y with a | | | | segmented | | | | distribution in Z for | | | | a cuboid defined by | | | | XSM, XSP, YSM, YSP, | | | | ZSM, and ZSP | | +-----------------------+-----------------------+-----------------------+ | nst=9 | Use a mesh source | Not supported | | | lite file | | +-----------------------+-----------------------+-----------------------+ .. _tab2-4a-8: .. table:: Supported array types for starting sources :align: center +--------------+-----------+ | no arrays | supported | +==============+===========+ | cuboid | supported | +--------------+-----------+ | hexagonal | supported | +--------------+-----------+ | shexagonal | no | +--------------+-----------+ | rhexagonal | no | +--------------+-----------+ | dodecahedral | no | +--------------+-----------+ The starting source initialized in Denovo is always a volumetric source---\ DEVC does not create point sources (which would activate the first collision option in Denovo). Sequence Output --------------- The main text output file consists of the output from the cross-section processing codes and Denovo. The user should examine the output and pay attention to any warnings or errors. :numref:tab2-4a-9 lists the files generated during the DEVC sequence. .. _tab2-4a-9: .. table:: Files created by DEVC for an input file named *input*.inp :align: center +-----------------+-----------------+-----------------+-----------------+ | **Filename** | | **Viewer** | **Description** | +=================+=================+=================+=================+ | Output Summary | | | | +-----------------+-----------------+-----------------+-----------------+ | | *input*.out | | main text | | | | | output file, | | | | | contains | | | | | :math:k_{\math | | | | | rm{\text{eff}}}| | | | | | +-----------------+-----------------+-----------------+-----------------+ | | *input*.msg | | messages file | +-----------------+-----------------+-----------------+-----------------+ | | | | | +-----------------+-----------------+-----------------+-----------------+ | Denovo | | | | +-----------------+-----------------+-----------------+-----------------+ | | xkba_b.inp | V\ :sup:a | input file for | | | | | Denovo – if | | | | | this file is | | | | | renamed to have | | | | | | | | | | a \*.dsi | | | | | extension | | | | | (Denovo simple | | | | | input), it is | | | | | viewable | | | | | | | | | | in the Mesh | | | | | File Viewer | +-----------------+-----------------+-----------------+-----------------+ | | ft02f001 | | AMPX formatted | | | | | cross sections | | | | | for Denovo | +-----------------+-----------------+-----------------+-----------------+ | | *input*.mmt | V | macromaterial | | | | | table, use with | | | | | \*.dso or | | | | | \*.dsi file | +-----------------+-----------------+-----------------+-----------------+ | | | | | +-----------------+-----------------+-----------------+-----------------+ | | *input*.dff | V | Denovo fission | | | | | fluxes | +-----------------+-----------------+-----------------+-----------------+ | | *input*.dso | V | Denovo fission | | | | | source | | | | | distribution | +-----------------+-----------------+-----------------+-----------------+ | :sup:a\ V – c\| | | | | an be displayed | | | | | with the Mesh F\| | | | | ile Viewer. | | | | +-----------------+-----------------+-----------------+-----------------+ Using the mesh file viewer ~~~~~~~~~~~~~~~~~~~~~~~~~~ The Mesh File Viewer is a Java utility shipped with SCALE that is used for viewing mesh tallies from Monaco, as well as importance maps and mesh-based sources in MAVRIC. The Mesh File Viewer can be used with DEVC to view the Denovo input file (\*.dsi, showing the starting source), the Denovo output fission source distribution (\*.dso) file, or the Denovo output flux (\*.dff) file. With any Denovo file, material information for each voxel can be displayed. Users can use the graphical user interface to select colors for each material in the DEVC input and save them to a colormap text file (\*.cmp) for later use. For example, :numref:fig2-4a-6 shows a cask model that has 13 materials with the default colors assigned by the viewer. A better color map (uranium is yellow, steel is blue, etc.) and an image using that color map are also shown in :numref:fig2-4a-6. .. _fig2-4a-6: .. figure:: figs/DEVC/fig6.png :align: center :width: 500 Viewing material information with the Mesh File Viewer. If the Denovo input was made using the mixed macromaterials, that can also be shown with the Mesh File Viewer. When one of the mesh files is loaded and the geometry is displayed (e.g., the materials for a cask model shown in :numref:fig2-4a-7), there will be many values since each macromaterial is treated by the Java viewer as a separate material. Redefining the color map using the GUI is not realistic. A colormap needs to be defined for the original materials of the problem. For this example, there are 13 original materials, but when using macromaterials, 73 macromaterials are used in the discrete-ordinates model (as listed in the \*.mmt file). The colormap file should only contain values for the 13 original materials. When loading the colormap, a corresponding \*.mmt file can also be loaded. This will display mixed colors for the macromaterials, as shown in :numref:fig2-4a-7. The final result is an image where the colors for the different values of the geometry attribute (which in the above example is material) are mixed in the ratio of the macromaterial definition. .. _fig2-4a-7: .. figure:: figs/DEVC/fig7.png :align: center :width: 500 Viewing material information from a Denovo input file. Viewing the starting source ~~~~~~~~~~~~~~~~~~~~~~~~~~~ The Java MeshFileViewer (scale/cmds/meshview) can be used to visualize the Denovo binary stream input file to show materials and starting source strengths. An example is shown in :numref:fig2-4a-8. **Material Numbering** The cross sections produced by the SCALE cross-section mixing module ICE typically have a number of materials equal to the maximum material ID specified by the user in the “read composition” block. For a user input that contains materials 1, 3, and 5, the GIP-formatted cross-section file will contain five entries. For each lattice cell calculation that uses a cellmix= parameter, one more entry is contained in the GIP file. Hence, the GIP file does not contain the user’s value from the “cellmix=” parameter but instead numbers the cellmix materials sequentially starting from 1+maximum(material ID). The Denovo geometry input and macroMixTable file produced by DEVC are modified to match the GIP cross-section file. When viewing the Denovo binary input file with the Mesh File Viewer, the GIP numbering for materials will be seen. .. _fig2-4a-8: .. figure:: figs/DEVC/fig8.png :align: center :width: 500 Fine-mesh version of sample problem 8, showing the materials using macromaterial blending of UO\ :sub:2, MOX, clad, and water (left) and the starting source strength limited to cells with fissionable material (right). Sample Problems --------------- Sample problems have been made that correspond to the eight CSAS6 sample problems. In each problem, the KENO parameters block was commented out, a parameters block containing Denovo calculation parameters was added, and a grid geometry block was added. These sample problems use a coarse discretization and loose tolerances to obtain a short runtime. Users will typically use much finer discretization (mesh, quadrature) and higher fidelity parameter settings for real eigenvalue calculations. The voxelized geometry and starting source distribution are shown below in :numref:fig2-4a-9. Results for the sample problems are displayed in :numref:tab2-4a-10. The sample problems used QR 1/1, a P\ :sub:0 scattering expansion, a k tolerance of 0.001 and coarse meshes for speed. The higher fidelity runs used finer spatial meshes, default parameters of QR 2/2, *P*\ :sub:0 scattering expansion, and the default *k* tolerance (10:sup:-5). Results for the longer-time CSAS6 and higher fidelity Denovo calculations are shown in :numref:fig2-4a-10. .. _fig2-4a-9: .. figure:: figs/DEVC/fig9.png :align: center :width: 600 Denovo geometry (left) and starting source distribution (right) for the sample problems. .. _fig2-4a-10: .. figure:: figs/DEVC/fig10.png :align: center :width: 500 Fission source distributions computed by CSAS6 (left) and Denovo (right). .. list-table:: Sample problem results :name: tab2-4a-10 :align: center * - .. image:: figs/DEVC/tab10.png .. bibliography:: bibs/DEVC.bib