Software
DIF3D (Diffusion and Transport Theory Codes)

Standard Code Description
 NAME AND TITLE
DIF3D 10.0: Code System Using Variational Nodal Methods and Finite Difference Methods to Solve Neutron Diffusion and Transport Theory Problems.  CONTRIBUTOR
K. L. Derstine
Nuclear Engineering Division
Argonne National Laboratory, Argonne, Illinois 60439.  CODING LANGUAGE AND COMPUTER
Fortran 90 and C source code for Linux PCs, MacOSX and SUN, (C00784MNYCP00).  NATURE OF PROBLEM SOLVED
The DIF3D10.0 release revises the significantly expanded set of solution techniques using variational nodal methods introduced with DIF3D8.0/VARIANT8.0 release (distributed by RSICC as CCC649). The nodal option of DIF3D solves the multigroup steadystate neutron diffusion equation in two and threedimensional hexagonal and Cartesian geometries and solves the transport equation in twoand threedimensional Cartesian geometries. Eigen value, adjoint, fixed source and criticality (concentration) search problems are permitted as are anisotropic diffusion coefficients. 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.
The VARIANT option solves the multigroup steadystate neutron diffusion and transport equations in two and threedimensional 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.
Related and Auxiliary Programs: DIF3D reads and writes the standard interface files specified by the Committee on Computer Code Coordination (CCCC). DIF3D is included in the REBUS3 (distributed by RSICC as CCC653) code package and can thus be used to provide the neutronics solutions required in REBUS3 depletion calculations.  METHOD OF SOLUTION
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 matrix scheme equivalent to a synthetic diffusion acceleration method  RESTRICTIONS OR LIMITATIONS
Problem dimensions are all variable. Enough memory must be allocated 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. Recent improvements have mitigated this problem significantly, but large energy group calculations (>100 groups) are still limited.  TYPICAL RUNNING TIME
Most of the 30 test cases were completed in a few seconds with a combined total time of 7 minutes for the benchmark suite. Two cases, bench20 and bench28 respectively, took 2 and 3 minutes. The existing coding only operates on a single core with no parallelism or threading.  COMPUTER HARDWARE REQUIREMENTS
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.  COMPUTER SOFTWARE REQUIREMENTS
No special requirements are made on the operating system. The included installation procedure requires Fortran 90 and C compilers. With modifications 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 and Linux workstations. Although developed on the Cray and IBM 30xx, the current version is tailored to Sun, Linux and MacOSX platforms.  REFERENCES (References are in electronic format in file C784.PDF on the distribution
CD.)
 included in the RSICC document
K. L. Derstine, DIF3D: A Code to Solve One, Two, and ThreeDimensional FiniteDifference Diffusion Theory Problems, ANL8264, Argonne National Laboratory, Argonne, IL (1984).
R. D. Lawrence, The DIF3D Nodal Neutronics Option for Two and ThreeDimensional Diffusion Theory Calculations in Hexagonal Geometry, ANL831, 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, ANL95/40, Argonne National Laboratory, Argonne, IL (October 1995).
C. H. Adams, et.al., The Utility Subroutine Package Used by Applied Physics Division Export Codes, ANL833, Argonne National Laboratory, Argonne, IL (May 1992).  background information:
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 41 (1991).
R. D. Lawrence, “Progress in Nodal Methods for the Solution of the Neutron Diffusion and Transport Equations,” Prog. Nucl. Energy, 17, 3, 271 (1986).
D. O’Dell, “Standard Interface Files and Procedures for Reactor Physics Codes, Version IV,” LA6941MS, Los Alamos Scientific Laboratory (September 1977).
B. J. Toppel, A Users Guide for the REBUS3 Fuel Cycle Analysis Capability, ANL832, Argonne National Laboratory, Argonne, IL (1983 revised October 1990).
J. Y. Doriath, F. Malvagi, G. Palmiotti, J. M. Ruggieri, C. B. Carrico, E. E. Lewis, and G. Gastaldo, "Variational Nodal Method (VNM) to Solve 3D Transport Equation: Applications to EFR Design," Proceedings of Mathematical Methods and Supercomputing in Nuclear Applications, *I571*, Karlsruhe, Germany, (April 1993).
C. B. Carrico, E. E. Lewis, and G. Palmiotti, "ThreeDimensional Variational Nodal Transport Methods for Caretsian, Triangular and Hexagonal Criticality Calculations," /Nuclear Science and Engineering,/ *111*, pp. 168179, (June 1992).
C. B. Carrico and E. E. Lewis, "Variational Nodal Solution Algorithms for Multigroup Criticality Problems," Proc. Int. Topl. Mtg. Advances in Mathematics, Computations and Reactor Physics, Vol. 2, April 28May 2, 1991, Pittsburgh, Pennsylvania.
E. E. Lewis, C. B. Carrico, and G. Palmiotti, "Variational Nodal Formulation for the Spherical Harmoncis Equations," /Nuclear Science and Engineering,/ *122*, 194203 (1996)).
 included in the RSICC document
 CONTENTS OF CODE PACKAGE
Included are referenced documents (10.a in pdf format) on one CD which also contains a Unix tar file which includes source code, sample problem input and output, code dependent BCD and binary card image file descriptions, scripts, a README file, an internal memorandum describing the revised Variant formulations and an internal technical memorandum for the HMG4C homogenization software (both memoranda are in pdf format). 
DATE OF ABSTRACT
September 2011.  Sponsor:
U.S. Department of Energy, Office of Nuclear Energy, Science, and Technology
Last Modified: Wed, September 21, 2011 12:03 PM