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A Kinetics Code for Solving the Time-Dependent Diffusion Equation

Standard Code Description

  1. Coding Language and Computing Platforms
    Fortran source code for Linux.
  2. Description of Purpose
    The DIF3D-K code solves the multigroup time-dependent neutron diffusion equations with or without an external neutron source. It is based upon DIF3D-Nodal and thus treats two- and three-dimensional hexagonal and Cartesian geometries. The point kinetics or spatial kinetics equations can be solved with DIF3D-K. The DIF3D-K code was built to function as part of an integrated dynamics code.

    The time-dependent multigroup neutron diffusion equations are discretized in both space and time. A nodal method employing one radial node per hexagonal assembly and one or more radial nodes per assembly in Cartesian geometry is used for spatial discretization. The nodal equations are derived using polynomial approximations to the spatial dependence of the flux within each node. The resulting equations are the time-dependent nodal equations for the neutron flux and precursor concentration moments, and the response matrix equations which relate the flux moments to the surface-averaged partial currents across nodal interfaces.

    The time-dependent nodal equations are solved with one of two major time discretization schemes: the theta method or the space-time factorization method. The theta method is a variable time integration scheme which permits the resulting difference equations to range from fully explicit to fully implicit. For a given value of the variable parameter Theta, the solution of the time-dependent nodal equations reduces to a sequence of ​“fixed source” problems in which the fixed source term is composed of quantities computed from the solution of the previous time point. In each fixed source problem, the unknown flux moments and interface partial currents are computed using a conventional fission source iteration accelerated by coarse-mesh rebalance and asymptotic source extrapolation. At each fission source iteration, the interface partial currents for each neutron energy group are determined from the response matrix equations with a known group source term.

    The factorization method allows the use of the improved quasistatic, adiabatic, or conventional point kinetics option for treatment of the time dependence. In the improved quasistatic option, the same algorithm (with Theta = 1) used for the theta scheme is employed with large time-step sizes to determine the flux shapes. In the adiabatic option a series of time-independent eigenvalue problems are employed to obtain the flux shapes. In the conventional point kinetics scheme, the initial steady-state shape is used for the duration of the transient problem. In all these factorization options, the flux amplitude is obtained from the solution of the point kinetics equations employing time-dependent kinetics parameters evaluated by the code.
  3. Typical Running Time
    The run time is strongly problem dependent and is greatly influenced by the number of neutron energy groups and meshes, the perturbation induced, the amount of edit data requested, and the duration of the transient problem. A two neutron group, six precursor family problem with 1910 meshes (split into 10 axial planes) in hexagonal-Z employing the theta method with 100 time steps requires less than a minute on modern computing workstations.
  4. References
    1. K. L. Derstine, ​“DIF3D: A Code to Solve One-, Two-, and Three-Dimensional Finite Difference Diffusion Theory Problems,” ANL-82-64, Argonne National Laboratory, April 1984.
    2. 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.
    3. K. O. Ott and D. A. Meneley, ​“Accuracy of the Quasistatic Treatment of Spatial Reactor Kinetics,” Nuclear Science and Engineering36, p. 402, 1969.
    4. T. A. Taiwo and H. S. Khalil, ​“The DIF3D Nodal Kinetics Capability in Hexagonal-Z Geometry: Formulation and Preliminary Tests,” International Topical Meeting on Advances in Mathematics, Computations, and Reactor Physics, Pittsburgh, Pennsylvania, April 28 - May 2, 1991, p. 23.2 2-1, American Nuclear Society, 1991.
    5. T. A. Taiwo and H. S. Khalil, ​“An Improved Quasistatic Option for the DIF3D Nodal Kinetics Code,” Proceedings of the Topical Meeting on Advances in Reactor Physics, Charleston, South Carolina, March 8-11, 1992, p. 2-469, American Nuclear Society, 1992.
    6. M. H. Kim, T. A. Taiwo and H. S. Khalil, ​“Analysis of the NEACRP PWR Rod Ejection Benchmark Problems with DIF3D-K,” Proceedings of the Topical Meeting on Advances in Reactor Physics, Knoxville, Tennessee, April 11-15, 1994, p. II-281, American Nuclear Society, 1994.
    7. T. A. Taiwo, et al., ​“SAS-DIF3DK Spatial Kinetics Capability for Thermal Reactor Systems,” Proceedings of the Joint International Conference on Mathematical Methods and Super-computing for Nuclear Applications, Saratoga Springs, New York, October 5­9, Vol. 2, pp. 1082-1096, American Nuclear Society, 1997.
  5. Primary Authors
    T. A. Taiwo, H. S. Khalil, and K. L. Derstine
    Nuclear Science and Engineering Division, Argonne National Laboratory
  6. Materials Available
    Distribution of this material is restricted contact nera-​software@​anl.​gov for licensing and distribution information.
  7. Sponsor
    U.S. Department of Energy, Office of Nuclear Energy