DIF3D 11.2892: Code System Using Variational Nodal Methods and Finite Difference Methods to Solve Neutron Diffusion and Transport Theory Problems.

Argonne National Laboratory, Argonne, Illinois.

Fortran 90 and C source code for Linux PCs, MacOSX and SUN (C00784MNYCP02)

The DIF3D 11.2892 release revises the performance and accuracy issues associated with the solution techniques of the variational nodal methods introduced in DIF3D8.0/VARIANT8.0 release (distributed by RSICC as CCC-649). The VARIANT option solves the diffusion or transport equations in two-and three-dimensional hexagonal and Cartesian geometries. Eigenvalue, adjoint, fixed source and criticality (concentration) search problems are permitted as are anisotropic diffusion coefficients. Flux and power density maps by mesh cell and region-wise balance integrals are provided. Although primarily designed for fast reactor problems, upscattering and, for the finite difference option only, internal black boundary conditions are also treated.

VARIANT solves the multigroup steady-state neutron diffusion and transport equations in two- and three-dimensional Cartesian and hexagonal geometries using variational nodal methods. The transport approximations involve complete spherical harmonic expansions up to order P99. Eigenvalue, adjoint, fixed source, gamma heating, and criticality (concentration) search problems are permitted. Anisotropic scattering is treated, and although primarily designed for fast reactor problems, upscattering options are also included. A transport based fixed source file was added to accommodate sensitivity calculations.

Related and Auxiliary Programs: DIF3D reads and writes the standard interface files specified by the Committee on Computer Code Coordination (CCCC). Additional utilities are provided to allow users to better use the existing software package including a basic visualization capability called DIF3D_TO_VTK which generates input files for VISIT or Paraview.

The neutron diffusion and transport equations are solved using a variational nodal method with one mesh cell (node) per hexagonal assembly (Cartesian geometry node sizes are specified by the user). The nodal equations are derived from a functional incorporating nodal balance, and reflective and vacuum boundary conditions through Lagrange multipliers. Expansion of the functional in orthogonal spatial and angular (spherical harmonics) polynomials leads to a set of response matrix equations relating partial current moments to flux and source moments. The equations are solved by fission source iteration in conjunction with a coarse mesh rebalance acceleration scheme. The inner iterations are accelerated by a partitioned diffusive matrix scheme. The Tchebychev acceleration was introduced to replace the coarse mesh rebalance and fission source extrapolation techniques the latter of which were both found to be unstable for both the forward and adjoint. The Omega acceleration was also corrected along with problems with the partial current mapping to improve solution accuracy.

Problem dimensions are all variable. Enough memory must be assigned to contain all the information for at least one energy group. Flux and source expansions of up to 99th order are allowed. Partial current expansions up to 9th order are allowed. Angular expansions of up to P99 are allowed. The typical limiting factor for a problem lies in the storage of response matrices for problems involving large numbers of unique node types. For highly heterogeneous problems involving thousands of different node types, calculation and storage of response matrices represent the primary limit to performing the calculation. In DIF3D 10.0, this was all forced to be stored as part of the BPOINTER software. In DIF3D 11.2892, the LMA software was added to DIF3D to facilitate memory sizes >> 100 GB for the VARIANT option. While the serial nature of the code still limits its performance on large energy group calculations, our work indicates that typical fast spectrum reactor models can be carried out with 230 group, P7 transport, a P5 scattering kernel, spatial 6th order flux and source and 1st order leakage in less than a day.

Most of the 34 test cases complete in a few seconds with a combined total time of 8 minutes for the benchmark suite where benchmarks 21, 24, and 27 take the longest times of 2:49, 1:45, and 1:59 minutes, respectively. The existing coding only operates on a single core with no parallelism or threading noting that we are working towards using limited threading for DIF3D 12.0.

External data storage must be available for approximately 40 scratch and interface files. If insufficient memory resources are available then large random access scratch files may be created which are associated with the individual response matrices and vectors used for the solution. We strongly recommend mounting a separate hard drive as /tmp and running all jobs from that location to prevent network drive issues. The remaining binary files are sequential access files with formatted or unformatted record types.

No special requirements are made on the operating system. The included installation procedure requires a Fortran 90 (or newer) compiler and we impose compile-time fixed memory sizes (see installation README.txt). We note that the code was originally built to allow limited dynamic memory sizing (up to 2 GB) which was eliminated due to multi-platform issues. Although developed on the Cray and IBM 30xx, the current version is tailored for execution on Linux and MacOSX platforms.

At this point we have support for intel and gnu compilers noting that REBUS does not work with several older versions of intel and the gcc compiler 4.1.2.

K. L. Derstine, DIF3D: A Code to Solve One-, Two-, and Three-Dimensional Finite-Difference Diffusion Theory Problems, ANL-82-64, Argonne National Laboratory, Argonne, IL (1984).

R. D. Lawrence, The DIF3D Nodal Neutronics Option for Two- and Three-Dimensional Diffusion Theory Calculations in Hexagonal Geometry, ANL-83-1, Argonne National Laboratory, Argonne, IL (1983).

G. Palmiotti, E. E. Lewis, and C. B. Carrico,
VARIANT: VARIational Anisotropic Nodal Transport for Multidimensional Cartesian and
Hexagonal Geometry Calculation, ANL-95/40, Argonne National Laboratory, Argonne, IL
(October 1995).

C. H. Adams, et.al., The Utility Subroutine Package Used by Applied Physics Division
Export Codes, ANL-83-3, Argonne National Laboratory, Argonne, IL (May 1992).

D. O’Dell, “Standard Interface Files and Procedures for Reactor Physics Codes,
Version IV,” LA-6941-MS, Los Alamos Scientific Laboratory (September 1977).

Included is a Unix tar file which includes source code, code documentation (in pdf format), sample problem input and output, code dependent BCD and binary card image file descriptions, python scripts, a README installation file, an updated manual describing the revisions to the Variant option

February 2014

**KEYWORDS:** DIFFUSION
THEORY; ASSEMBLY HOMOGENIZED TRANSPORT SOLVER; MULTIGROUP; CRITICALITY CALCULATIONS;
CCCC INTERFACE FORMAT; REACTOR PHYSICS