# Software

## DIF3D-K (Diffusion and Transport Theory Codes)

### Standard Code Description

**Name of Program:**

DIF3D-K 1.5: A Nodal Kinetics Code for Solving the Time-Dependent Diffusion Equation.**Computer for Which Program is Designed and Other Machine Version Packages Available:**

Cray computers using UNICOS, and UNIX-based workstations.**Description of Problem Solved:**

The DIF3D-K code solves the multigroup time-dependent neutron diffusion equations (with or without an external neutron source) in two- and three-dimensional hexagonal and Cartesian geometries. All steady-state calculational options of the base time- independent DIF3D 6.1 code[1,2] are retained.**Method of Solution:**

The time-dependent 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 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[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 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.**Restrictions on the Complexity of the Problems:**

The time-dependent capability is limited to nodal calculations in two- and three-dimensional hexagonal and Cartesian geometries. Computer memory sufficient to core-contain all data for at least one energy group is required. Although the code contains no thermal-hydraulics 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, hexagonal-Z problem employing the theta method with 100 time steps requires about 84 cpu seconds on the Cray X-MP/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 time-dependent nodal equations with large time steps, as opposed to solving a shape equation with the large time steps[3].**Related and Auxiliary Programs:**

The DIF3D-K code is designed to facilitate its incorporation into an integrated dynamics code.**Status:**

The DIF3D-K 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 Three-Dimensional Finite Difference Diffusion Theory Problems," Argonne-82-64, Argonne National Laboratory, April 1984.
- R. D. Lawrence, "The DIF3D Nodal Neutronics Option for Two- and Three-Dimensional Diffusion Theory Calculations in Hexagonal Geometry," Argonne-83-1, 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 Hexagonal-Z Geometry: Formulation and Preliminary Tests." Int. Topl. Mtg. on Advances in Mathematics, Computations, and Reactor Physics, Pittsburgh, Pennsylvania, April 28-May 2, 1991, p. 23.2 2-1, 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 8-11, 1992, p. 2-469, American Nuclear Society (1992).
- M. H. Kim, T. A. Taiwo and H. S. Khalil, "Analysis of the NEACRP PWR Rod Ejection Benchmark Problems with DIF3D-K," Proc. Topl. Mtg. on Advances in Reactor Physics, Knoxville, Tennessee, April 11-15, 1994, p. II-281, American Nuclear Society (1994).
- 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).

**Machine Requirements:**

The executable code module has a program length of about 755,000 words on the Cray X-MP 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 X-MP computer, and about 2 Megabytes of storage on the SUN 20/50 and IBM RISC 6000/350 workstations.**Programming Languages Used:**

FORTRAN 77. DIF3D-K 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

**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, April 20, 2016 9:52 AM