Argonne National Laboratory

Nuclear Science and Engineering

DIF3D

A Code to Solve Steady State Neutron Diffusion and Transport Theory Problems

Standard Code Description

  1. Coding Language and Computing Platforms
    Fortran source code for Linux, Macintosh, and Microsoft Windows.
  2. Description of Purpose
    The DIF3D code (DIFfusion 3D) has been a workhorse of fast reactor analysis work at Argonne National Laboratory for over 40 years (references [1] through [6]). DIF3D was primarily built as a three-dimensional solver of the multi-group diffusion equation for semi-structured grid geometries (references [1] through [3]). The diffusion equation, with proper cross section data, has proven to be a reliable means to predict the fuel cycle behavior of thermal and fast spectrum nuclear reactors. The DIF3D code was built in the late 1970s using a finite difference spatial differencing methodology applied to the diffusion equation which we refer to today as DIF3D-FD. Later, in the early 1980s, a transverse integrated nodal methodology, referred to as DIF3D-Nodal [4], was built into DIF3D to improve the performance on large scale reactor problems. Finally, to support a research design goal of developing fast spectrum reactors that promote non-proliferation by eliminating blanket assemblies, the DIF3D-VARIANT solver (references [5] through [6]) was added to DIF3D in the mid-1990s that extends the concept of DIF3D-Nodal to a functional three-dimensional transport code based upon spherical harmonic expansions in angle.

    Over its 40-year history, DIF3D has been applied to numerous fast and thermal spectrum reactor analysis projects. For those cases with experimental measurements, DIF3D performed exceptionally well, yielding results of consistent accuracy to those produced by the Monte Carlo method at a fraction of the cost. With all of these successes, it is important to point out that DIF3D does have limitations for general purpose usage for geometrically non-regular systems.

    The present DIF3D capability can treat slab and cylindrical 1D domains, Cartesian, hexagonal, and R-Z two-dimensional domains, and Cartesian, hexagonal-Z, triangular-Z, and R-Z-θ three-dimensional domains. The DIF3D-FD solver is based upon the finite difference approximation of the diffusion equation. This solver can be applied to every geometry type in DIF3D except for hexagonal and hexagonal-Z geometries. As mentioned, the DIF3D-Nodal solver was added for improved performance but only for Cartesian, hexagonal, and hexagonal-z geometries. The DIF3D-VARIANT solver provides an even-parity transport capability useful for high-leakage reactor configurations. DIF3D-VARIANT is also only implemented on Cartesian and hexagonal geometries.

    Eigenvalue, adjoint, fixed source and criticality (concentration and geometry) search problems are permitted as are anisotropic diffusion coefficients. Flux and power density maps by mesh cell and region-wise balance integrals are produced. Although primarily designed for fast reactor problems, upscattering and internal black boundary conditions can be used.

    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 REBUS codeand can thus be used to provide the neutronics solutions required in REBUS depletion calculations.
  3. Typical Running Time
    Most of the provided test cases were completed in less than a minute. The combined test suite requires less than 10 minutes on a modern workstation. DIF3D is a serial code that does not contain any parallelism or threading.
  4. References
    1. Included in the RSICC document:
      • R. D. Lawrence, ​“Progress in Nodal Methods for the Solution of the Neutron Diffusion and Transport Equations,” Prog. Nucl. Energy, 17, 271, 1986.
      • M. R. Wagner, ​“Three-Dimensional Nodal Diffusion and Transport Theory for Hexagonal-z Geometry,” Nucl. Sci. Eng., 103, 377-391, 1989.
      • K. L. Derstine, ​“DIF3D: A Code to Solve One-, Two-, and Three-Dimensional Finite-Difference Diffusion Theory Problems,” ANL-82-64, Argonne National Laboratory, 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, March 1983.
      • G. Palmiotti, E.E. Lewis, C. B. Carrico, ​“VARIANT: VARIational Anisotropic Nodal Transport for Multidimensional Cartesian and Hexagonal Geometry Calculation,” ANL-95/40, Argonne National Laboratory, 1995.
      • M. A. Smith, E. E. Lewis, E. R. Shemon, ​“DIF3D-VARIANT 11.0, A Decade of Updates,” ANL/NE-14/1, 2014.
    2. 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 4-1, 1991.
      • D. O’Dell, ​“Standard Interface Files and Procedures for Reactor Physics Codes, Version IV,” LA-6941-MS, Los Alamos Scientific Laboratory, September 1977.
      • B. J. Toppel, ​“A Users Guide for the REBUS-3 Fuel Cycle Analysis Capability,” ANL-83-2, Argonne National Laboratory, 1983, revised October 1990.
      • C. B. Carrico, E. E. Lewis, and G. Palmiotti, ​“Three-Dimensional Variational Nodal Transport Methods for Caretsian, Triangular and Hexagonal Criticality Calculations,” Nuclear Science and Engineering, 111, pp. 168­179, June 1992.
      • E. E. Lewis, C. B. Carrico, and G. Palmiotti, ​“Variational Nodal Formulation for the Spherical Harmoncis Equations,” Nuclear Science and Engineering, 122, 194-203, 1996.
  5. Primary Authors
    • K. L. Destine, Argonne National Laboratory
    • R. D. Lawrence, Argonne National Laboratory
    • G. Palmiotti, Idaho National Laboratory
  6. Materials Available
    The source code and compilation instructions are provided. Precompiled executables for Linux and Macintosh are also included. The source code and executables for all utility programs associated with the Argonne Reactor Code system are also included. Documentation on all solvers in DIF3D is provided along with all of the verification test cases for DIF3D. Contact nera-​software@​anl.​gov for licensing and distribution information.
  7. Sponsor
    U.S. Department of Energy, Office of Nuclear Energy