**RSICC CODE PACKAGE CCC-676**

**1. NAME AND TITLE**

FESH: X-Y Multigroup Neutron Transport Code System.

**2. CONTRIBUTORS**

Northwestern University, Evanston, Illinois, and Argonne National Laboratory, Argonne, Illinois, through the Energy Science and Technology Science Center, Oak Ridge, Tennessee.

**3. CODING LANGUAGE AND COMPUTER**

Fortran IV; CDC6600 (C00676CDCMF00).

**4. NATURE OF PROBLEM SOLVED**

FESH (Finite Element Spherical Harmonics) solves the spherical harmonics approximation to the second-order multigroup neutron transport equation in two dimensions. A three-dimensional spherical harmonics approximation of user-specified order is applied to the angular variable and two-dimensional spatial finite elements to the spatial variable. Scattering is assumed to be isotropic. Either multiplication eigenvalue problems or subcritical inhomogeneous source problems can be solved with several combinations of vacuum and reflective boundary conditions possible.

**5. METHOD OF SOLUTION**

FESH solves the multigroup transport equations (outer iterations) using a power iteration technique on the fission source with coarse mesh rebalance acceleration. The within-group (inner iteration) equation is solved by a block successive overrelaxation method with coarse mesh rebalance acceleration available as an option. Each block represents coupling and source information for each spatial mesh point.

**6. RESTRICTIONS OR LIMITATIONS**

Sources and scattering are assumed to be isotropic; up-scattering is not allowed. Flexible dimensioning permits combinations of problem parameters to occupy an array of 50,000 words. Most group-dependent data is stored in extended core storage (ECS).

**7. TYPICAL RUNNING TIME**

The time required for execution is problem-dependent. NESC executed the sample problem in 80 CP seconds on a CDC6600 and 20 CP seconds on a CDC7600.

**8. COMPUTER HARDWARE REQUIREMENTS**

FESH ran on CDC mainframe computers and required 200,000 (octal) words of central memory and 142,000 (octal) words of ECS to execute the program. Central memory requirements for single precision arithmetic may be estimated as (45M+10) * (L(L+1)/2)**2 + NSP*((L(L+1)/2)+2) words, where M is the number of material regions, L is the order of the spherical harmonics approximation, and NSP is the number of spatial mesh points.

**9. COMPUTER SOFTWARE REQUIREMENTS**

FESH was developed under the SCOPE operating system and requires a Fortran IV compiler. FESH was tested when initially packaged by NESC in 1980 but was not tested when it was transferred to RSICC and released in April 2001.

**10. REFERENCE**

R. N. Blomquist and E. E. Lewis, "Instruction Manual for the Computer Code FESH: Finite Element Spherical Harmonics," Northwestern University memorandum (March 1978).

**11. CONTENTS OF CODE PACKAGE**

Included in the package are the referenced document and a DOS formatted diskette containing source code and a sample problem. No executables are included in the package.

**12. DATE OF ABSTRACT**

April 2001.

** KEYWORDS:** FINITE ELEMENT METHOD; MULTIGROUP; SPHERICAL
HARMONICS