**
1. NAME AND TITLE**

LABAN-PEL: A Two-Dimensional, Multigroup Diffusion, High-Order Response Matrix Code.

**2. CONTRIBUTOR**

Atomic Energy Corporation of South Africa (Ltd), Pretoria, Republic of South Africa.

**3. CODING LANGUAGE AND COMPUTER**

Fortran 77, IBM 370 and IBM PC.

**4. NATURE OF PROBLEM SOLVED**

The two-dimensional Cartesian geometry multigroup diffusion equations are solved by means of the high-order response matrix method. The method is applied to coarse-mesh problems and is useful as a benchmarking tool for nodal methods.

**5. METHOD OF SOLUTION**

The spatial shapes of partial currents on nodal (coarse-mesh) faces are expanded in
terms of Legendre polynomials and the nodal response matrices are generated via a
Fourier series method. The response matrices include both scattering and fission
processes, so that they are implicitly dependent on the Keff for the problem. An explicit
eigenvalue problem in which all energy groups are treated simultaneously, is solved by
means of the power method. The implicit eigenvalue (Keff) is determined by means of a
*regula falsi* method which yields an explicit eigenvalue of unity.

**
6. RESTRICTIONS OR LIMITATIONS**

LABAN-PEL is restricted to the solution of 2-D diffusion problems but, since it is a variably dimensioned code, there are no other restrictions (e.g. on number of energy groups). The size of the problem is restricted only by the computer core storage available.

**7. TYPICAL RUNNING TIME**

The running time for a typical 2-group problem such as the 2-D IAEA Benchmark Problem using a P4 approximation (reference quality solution) is of the order of 4 minutes on a 33MHz i80386 PC with an i80387 mathematics co-processor.

**8. COMPUTER HARDWARE REQUIREMENTS**

LABAN-PEL has run routinely on IBM mainframes and on 32-bit 80386/80486 class personal computers.

**9. COMPUTER SOFTWARE REQUIREMENTS**

The code is written in FORTRAN 77 and has run under MVS on IBM mainframes. The executable file for the PC included in the package was created with the Lahey F77L-EM-32 Version 5.0 compiler. The code has also run on 32 bit PC's under the UNIX operating system with the lpi compiler. Machine-dependent OPEN statements are the only required changes.

**10. REFERENCES**

E. Z. Muller, "LABAN-PEL: A Two-Dimensional, Multigroup Diffusion, High-Order Response Matrix Code," PEL-309 (June 1991).

E. Z. Muller, Z. J. Weiss, "Benchmarking with the Multigroup Diffusion High-Order Response Matrix Method," *Ann. nucl. Energy, 18, 535-544* (1991).

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**
11. CONTENTS OF CODE PACKAGE**

Included in the package are the referenced documents and 1 DS/HD diskette which includes the source files, PC executable file, test case input data and output written in DOS format.

**12. DATE OF ABSTRACT**

March 1993.

**KEYWORDS:** DIFFUSION THEORY, MICROCOMPUTER