NEA-0905 SIXTUS-2.

1. NAME OR DESIGNATION OF PROGRAM:  SIXTUS-2.

3. DESCRIPTION OF PROBLEM OR FUNCTION

Coarse mesh solution to the steady state multigroup neutron diffusion equation in two dimensional array of regular hexagons.

4. METHOD OF SOLUTION

A solution in terms of face averaged partial currents and node averaged flux is obtained from the response matrix equations for irreducible symmetry components of partial currents at nodal interfaces. The response matrix elements are generated from the base set of analytical fundamental solutions spanned on an exact spectrum of the node reaction matrix. The RM equations are solved by an explicit scheme in which all the nodes are scanned in a pre- scribed order and the energy group vector of outgoing currents is used to form the irreducible symmetry components of the energy group vector of incoming currents for neighboring nodes. The effective multiplication constant is iterated directly from the neutron balance. Because the method does not use a conventional group-by- group solution but deals with all energy groups simultaneously, the  presence of upscattering does not influence adversely the convergence rate. This iteration is accelerated by Lyusternik-Wagner extrapolation of currents and flux values.

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

(1) The problem size designated LIM should not exceed 12000. This     number, however, can be readily increased.
(2) External sources are not permitted, only eigenvalue (keff)     solutions.
(3) Because of rounding error problems the number of energy groups     should not exceed 10 for the present version of the program.

6. TYPICAL RUNNING TIME

About 2.4 milliseconds of CP time on CDC6400  per one sweep, node and group. To reach an accuracy of the order of  10**(-7) for keff and fission source and 10**(-6) for nodal flux, the code requires 80 to 120 sweeps depending on the nature of the problem.
NEA-DB executed the test case on CDC CYBER 174 in 151 CPU seconds.

7. UNUSUAL FEATURES OF THE PROGRAM

(1) Fairly arbitrarily connected arrangement of hexagonal nodes.  Symmetry 360 degree as well as 60 degree sectors with both     reflectional and periodical symmetries are allowed.
(2) Total group and node balance tables are provided as output.

8. RELATED AND AUXILIARY PROGRAMS:  A two-dimensional program SIXTUS2.

10. REFERENCES

- J.J. Arkuszewski:
  "A Solution to the Benchmark Problem ID9-A1 of the Benchmark
   Problem Book"
   EIR Internal Report TM-22-82-19 (1982)

- J.J. Arkuszewski:
  SIXTUS-2 - A Two Dimensional Multigroup Diffusion Theory Code in
  Hexagonal Geometry. Part 1: Theory, Code Description and User's
  Manual.  EIR-Bericht 470  (September 1982).
- J.J. Arkuszewski:
  SIXTUS-2 - A Two Dimensional Multigroup Diffusion Theory Code in
  Hexagonal Geometry. Part 2: Code Validation.
  EIR-Bericht 471  (September 1982).

11. MACHINE REQUIREMENTS

Main storage of 70,000 octal words. Mass storage file TAPE10 as scratch file. When catalogued, this file makes available on records 2 and 3 two arrays of nodal fluxes and partial currents for two consecutive iterations.

13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED

Standard NOS/BE.  The program contains several routines from the EISPACK package.

14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

Installation of the program on computers with shorter than 60-bit word length may require a replacement of EISPACK routines for the algebraic eigenvalue problem of a real general matrix. The same pertains to the general matrix inversion algorithm (routine TRIX).

15. NAME AND ESTABLISHMENT OF AUTHOR

          Jacek J. Arkuszewski
          Paul Scherrer Institute 106/22
          CH-5232 Villigen-PSI, Switzerland

File name	File description	Records
NEA0905_01.003	SIXTUS-2 INFORMATION FILE	44
NEA0905_01.004	SIXTUS-2 SOURCE CARD-IMAGES (FORTRAN-4)	2394
NEA0905_01.005	SIXTUS-2 JCL FOR TEST CASE EXECUTION	22
NEA0905_01.006	SIXTUS-2 INPUT DATA FOR TEST CASE	82
NEA0905_01.007	SIXTUS-2 OUTPUT OF TEST CASE	1012