1. Name of Program:
   DIF3D 7.0
2. Computer for Which Program is Designed and Other Machine Version Packages Available:
   Unix Workstations (Sun SparcStation, IBM RS6000), CRAY X-MP & IBM 30xx.
3. Description of Problem Solved:
   DIF3D's nodal option solves the multigroup steadystate neutron diffusion and (for cartesian geometry only) transport equations in two- and three-dimensional hexagonal and cartesian geometries. One-, two- and three-dimensional orthogonal( rectangular and cylindrical) and triangular geometry diffusion theory problems are solved by DIF3D's finite difference option. Eigenvalue, adjoint, fixed source and criticality (concentration) search problems are permitted. Anisotropic diffusion coefficients are permitted. Flux and power density maps by mesh cell and regionwise balance integrals are provided. Although primarily designed for fast reactor problems, upscattering and (for finite difference option only) internal black boundary conditions are also treated.
4. Method of Solution:
   Nodal Option: the neutron diffusion equation is solved using a nodal scheme (Refs. 1, 2) with one mesh cell (node) per hexagonal assembly (Cartesian geometry node sizes are specified by the user). The nodal equations are derived using higher order polynomial approximations to the spatial dependence of the flux within the (hexagonal or Cartesian) node. The final equations, which are cast in response matrix form, involve spatial moments of the node-interior flux distribution plus surface-averaged partial currents across the faces of the node. These equations are solved using a fission source iteration with coarse-mesh rebalance acceleration. Equivalence Theory parameters (Ref. 3) (discontinuity factors) are permitted with hexagonal nodal models. Finite Difference Option: mesh-centered finite-difference equations are solved by optimized iteration methods (Ref. 4). A variant of the Chebyshev semi-iterative acceleration technique is applied to outer (fission source) iterations, and an optimized block-successive-overrelaxation method is applied to the within-group iterations. Optimum overrelaxation factors are precomputed for each energy group prior to the initiation of the outer iterations. The forward sweep of the LU decomposition algorithm for the resulting tridiagonal matrices is computed prior to outer iteration initiation in orthogonal non-periodic geometry cases.
5. Restrictions on the Complexity of the Problems:
   Problem dimensions are all variable. Enough memory must be available to contain all data for at least one energy group. In three dimensional finite difference option problems, a concurrent inner iteration strategy permits the specification of an unlimited number of planes. Scattering is P₀ only.
6. Typical Running Time:
   A three-dimensional nodal calculation for a small LMR with 60 planar symmetry, 9 energy groups, 14 axial mesh planes and 16 rings of hexagons required 22 CPU seconds on a Sun SPARCstation 20 (61 seconds on a SPARCStation 5, 18 seconds on an IBM RS6000) to perform 14 outer iterations with 28 inners/outer and a convergence criteria of 10-6. A similar problem required 8 CPU seconds on a CRAY X-MP/14 for 12 outer iterations with 24 inners/outer.
7. Unusual Features of the Program:
   DIF3D Nodal option uses a single meshpoint per hexagon instead of the six triangular mesh points per hexagon typically enployed in fast reactor finite difference calculations. The higher-order axial approximation (Refs. 2, 3) permits the use of coarse axial meshes without sacrificing accuracy. Then nodal coupling coefficients are precomputed and stored only for unique nodes. The isotropic-leakage assumption is the dominant source of error for the nodal transport scheme. Equivalence Theory (discontinuity factors) may be used in the hexagonal geometry nodal option.
8. Related and Auxiliary Programs:
   DIF3D reads and writes the standard interface files specified by the Committee on Computer Code Coordination5 (CCCC). DIF3D is included in the REBUS-3 code package (Ref. 6) and can thus be used to provide the neutronics solutions required in REBUS-3 depletion calculations.
9. Status:
   The modular version of the code is in production use at Argonne National Laboratory on Unix Workstations (Sun SPARCStation Models 5 and 20, and IBM RS6000).
10. References:
    1. R.D. Lawrence, "Progress in Nodal Methods for the Solution of the Neutron Diffusion and Transport Equations," Prog. Nucl. Energy, 17, 3, 271 (1986).
    2. R. D. Lawrence, "The DIF3D Nodal Neutronics Option for Two- and Three-Dimensional Diffusion Theory Calculations in Hexagonal Geometry, Argonne-83-1, Argonne National Laboratory (1983).
    3. P. J. Finck and K. L. Derstine,"The Application of Nodal Equivalence Theory to Hexagonal Geometry Lattices", Proceedings of the International Topical Meeting Advances in Mathematics, Computations and Reactor Physics, Pittsburgh, Pa., Vol. 4, pp. 16.1 4-1 (1991).
    4. K. L. Derstine,"DIF3D: A Code to Solve One-, Two-, and Three-Dimensional Diffusion Theory Problems," Argonne-82-64, Argonne National Laboratory, (1984).
    5. Douglas O'Dell, "Standard Interface files and Procedures for Reactor Physics Codes, Version IV," UC-32, Los Alamos Scientific Laboratory, September, (1977).
    6. B.J. Toppel, "A Users Guide for the REBUS-3 Fuel Cycle Analysis Capability," Argonne National Laboratory, Argonne-83-2, Argonne National Laboratory (1983).
11. Machine Requirements:
    At least 16 Mbytes of RAM are recommended for program and file buffer storage on a Unix Workstation. External data storage must be available for approximately 40 scratch and interface files. Fourteen of these files are random access scratch files (grouped into 6 file groups) and the remainder are sequential access files with formatted or unformatted record types.
12. Programming Languages Used:
    FORTRAN `77 is used. The program can be executed entirely in FORTRAN. Optional dynamic memory allocation and timing routines supplied from host machine libraries or code in "C" may be used on Unix workstations and the CRAY XMP.
13. Operating System:
    No special requirements are made on the operating system. SunOS 4.1.3x and SOLARIS 2.5 (for SPARCStations), AIX 3.2 on the IBM RS6000, the XMP UNICOS operating system segmentation loader (segldr) and the IBM (MVS/JES3) linkage editor overlay facilities may be used.
14. Other Programming or Operating Information or Restrictions:
    The standalone source code contains approximately 109,000 FORTRAN statements and 444 C statements.
15. Name and Establishment of Author or Contributor:
    • K. L. Derstine
      Nuclear Engineering Division
      Argonne National Laboratory
      9700 South Cass Avenue
      Argonne, Illinois 60439
16. Materials Available:
    Distribution of this material may be restricted.
    
    • Electronic Media UNIX "tar" file including
    • Source Code
    • Sample Problem Data Card-Images
    • Sample Problem Output
    • Code Dependent BCD and Binary Card Image File Descriptions
    • Segmentation Loader Control Statements
    • Reference reports, Argonne-82-64, Argonne-83-1, and Argonne-83-3 in PDF form
    • Export Note
17. Sponsor:
    U.S. Department of Energy, Office of Nuclear Energy, Science, and Technology.

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