Software
DIF3DK (Diffusion and Transport Theory Codes)

Standard Code Description
 Name of Program:
DIF3DK 1.5: A Nodal Kinetics Code for Solving the TimeDependent Diffusion Equation.  Computer for Which Program is Designed and Other Machine Version Packages Available:
Cray computers using UNICOS, and UNIXbased workstations.  Description of Problem Solved:
The DIF3DK code solves the multigroup timedependent neutron diffusion equations (with or without an external neutron source) in two and threedimensional hexagonal and Cartesian geometries. All steadystate calculational options of the base time independent DIF3D 6.1 code[1,2] are retained.  Method of Solution:
The timedependent multigroup neutron diffusion equations are discretized in both space and time. A nodal method[2] 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 timedependent nodal equations for the neutron flux and precursor concentration moments, and the response matrix equations which relate the flux moments to the surfaceaveraged partial currents across nodal interfaces.
The timedependent nodal equations are solved with one of two major time discretization schemes: the theta method or the spacetime 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 timedependent 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 coarsemesh 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[3], 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 timestep sizes to determine the flux shapes. In the adiabatic option a series of timeindependent eigenvalue problems are employed to obtain the flux shapes. In the conventional point kinetics scheme, the initial steadystate 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 timedependent kinetics parameters evaluated by the code.  Restrictions on the Complexity of the Problems:
The timedependent capability is limited to nodal calculations in two and threedimensional hexagonal and Cartesian geometries. Computer memory sufficient to corecontain all data for at least one energy group is required. Although the code contains no thermalhydraulics feedback models, it can be implemented as a code module in a dynamics code.  Typical Running Time:
The running time is strongly problem dependent and is greatly influenced by the number of neutron energy groups and nodes, the perturbation induced, the amount of edit data requested, and the duration of the transient problem. A 2 neutron group, 6 precursor family, 1910 node (10 axial planes), sixth core, hexagonalZ problem employing the theta method with 100 time steps requires about 84 cpu seconds on the Cray XMP/18 computer. This same job requires about 87 and 143 cpu seconds on the IBM RISC 6000/350 and SUN 20/50 workstations, respectively.  Unusual Features of the Program:
Availability of multiple solution options (theta and factorization methods). The improved quasistatic scheme obtains the flux shapes by solving the timedependent nodal equations with large time steps, as opposed to solving a shape equation with the large time steps[3].  Related and Auxiliary Programs:
The DIF3DK code is designed to facilitate its incorporation into an integrated dynamics code.  Status:
The DIF3DK kinetics solution options have been verified by solving analytical test cases, benchmark problems, and numerical and experimental test cases[47].  References:
 K. L. Derstine, "DIF3D: A Code to Solve One, Two, and ThreeDimensional Finite Difference Diffusion Theory Problems," Argonne8264, Argonne National Laboratory, April 1984.
 R. D. Lawrence, "The DIF3D Nodal Neutronics Option for Two and ThreeDimensional Diffusion Theory Calculations in Hexagonal Geometry," Argonne831, Argonne National Laboratory, March 1983.
 K. O. Ott and D. A. Meneley, "Accuracy of the Quasistatic Treatment of Spatial Reactor Kinetics," Nuclear Science and Engineering, 36, p. 402, (1969).
 T. A. Taiwo and H. S. Khalil, "The DIF3D Nodal Kinetics Capability in HexagonalZ Geometry: Formulation and Preliminary Tests." Int. Topl. Mtg. on Advances in Mathematics, Computations, and Reactor Physics, Pittsburgh, Pennsylvania, April 28May 2, 1991, p. 23.2 21, American Nuclear Society (1991).
 T. A. Taiwo and H. S. Khalil, "An Improved Quasistatic Option for the DIF3D Nodal Kinetics Code," Proc. Topl. Mtg. on Advances in Reactor Physics, Charleston, South Carolina, March 811, 1992, p. 2469, American Nuclear Society (1992).
 M. H. Kim, T. A. Taiwo and H. S. Khalil, "Analysis of the NEACRP PWR Rod Ejection Benchmark Problems with DIF3DK," Proc. Topl. Mtg. on Advances in Reactor Physics, Knoxville, Tennessee, April 1115, 1994, p. II281, American Nuclear Society (1994).
 T. A. Taiwo, et al., "SASDIF3DK Spatial Kinetics Capability for Thermal Reactor Systems," Proceedings of the Joint International Conference on Mathematical Methods and Supercomputing for Nuclear Applications, Saratoga Springs, New York, October 59, Vol. 2, pp. 10821096, American Nuclear Society (1997).
 Machine Requirements:
The executable code module has a program length of about 755,000 words on the Cray XMP computer. A HWR core model with 2 neutron energy groups, 6 precursor families, 14 compositions and 10 axial nodes requires about 307,000 storage words for execution on the Cray XMP computer, and about 2 Megabytes of storage on the SUN 20/50 and IBM RISC 6000/350 workstations.  Programming Languages Used:
FORTRAN 77. DIF3DK can be executed entirely in FORTRAN. Optional dynamic memory allocation routines are written in assembler language or C, or can be obtained from host machine libraries[1].  Operating System:
UNICOS on the Cray computer and UNIX on workstations.  Other Programming or Operating Information or Restrictions:
Some plotting routines are only active in the Argonne version of the code.  Name and Establishment of Author(s) or Contributor(s):
 T. A. Taiwo, H. S. Khalil, and K. L. Derstine
Nuclear Engineering Division
Argonne National Laboratory
9700 South Cass Avenue
Argonne, Illinois 60439
 T. A. Taiwo, H. S. Khalil, and K. L. Derstine
 Materials Available:
Distribution of this material may be restricted.
 Source Code
 Sample Problem Input
 Sample Problem Output
 User's Manual
 Sponsor:
U.S. Department of Energy, Office of Nuclear Energy, Science, and Technology.
Last Modified: Wed, September 21, 2011 12:03 PM