**
1. NAME AND TITLE**

SIXTUS-3: Three-Dimensional, Nodal, Neutron Diffusion Criticality Code System in Hex-Z Geometry.

**2. CONTRIBUTOR**

Paul Scherrer Institut, Switzerland and Osaka University, Yamada Oka, Suita Osaka, Japan.

**3. CODING LANGUAGE AND COMPUTER**

Fortran 77; CRAY, SUN, VAX

**4. NATURE OF PROBLEM SOLVED**

SIXTUS-3 is a 3D extention of SIXTUS-2 and is based on a response matrix nodal model. The code offers a fast and accurate analysis of critical systems in the regular hex-z geometry with the multigroup cross section representation including arbitrary upscattering.

**5. METHOD OF SOLUTION**

Intranodal elementary solutions with an exact multigroup eigenvalue spectrum are
spanned on two irreducible symmetry bases for the *C6* and *C2* groups of rotations for
lateral and axial components, respectively. They represent a general homogeneous
solution which is augmented with the special heterogeneous one determined by the
transversal leakage terms, and from it the multigroup nodal response matrix for the partial
current symmetry components on the node interfaces is computed. The response of a
node to the incoming current is propagated in the system in a node sweeping process, and
after a prescribed number of sweeps the multiplication factor and the response matrix are
recalculated. The iterations are terminated when the criteria of convergence for the
multiplication factor, fission source, and flux are met. An acceleration algorithm based on
a special version of the Lyusternik-Wagner extrapolation scheme is employed.

**6. RESTRICTIONS OR LIMITATIONS**

Number of materials should not exceed 255, however this restriction can be easily removed. Only criticality problems can be handled.

**7. TYPICAL RUNNING TIME**

ProblemRef.NodesGr.It./Sw.SecPerf.PlatformSNRAAEW-R 13461026430/110630.13SUN Sparc 2VVERZfK-5571848261/1231050.22SUN 4/390HTGRANL-74161248482/3183190.20SUN 4/390PROT-EUS15481387/1809520.26SUN 4/390

The performance parameter is defined as the iteration CPU time (milisec) per one node, group, and sweep.

**8. COMPUTER HARDWARE REQUIREMENTS**

A typical problem may need 20 kB to 1 MB for a container master array. SIXTUS-3 runs on Cray, Sun, or Vax computers.

**9. COMPUTER SOFTWARE REQUIREMENTS**

Either UPDATE, HISTORIAN or PSR-245/UPEML is required. RSIC used UPEML to create the Fortran 77 source for Sun workstations and included it in the package. The code ran under VMS on Vax computers, under UNICOS on Cray, and is expected to run on any UNIX platform.

**10. REFERENCES**

**a: included in documentation:**

J. J. Arkuszewski, "SIXTUS 3.0 Primer," PSI Memo TM-40-90-06/Rev. (1991).

J. J. Arkuszewski, Y. Kawagoe, T. Takeda, "SIXTUS-3: A Three Dimensional Diffusion Code in Hex-Z Geometry," Swiss PSI Report 102 (1991).

**b: background information:**

Y. Kawagoe, T. Takea, J. J. Arkuszewski, "Development of 3D Nodal Diffusion Code Based on Group Theory in Hexagonal-Z Geometry," Pittsburgh, Penn., Int. ANS Meeting on "Advances in Mathematics, Computations, and Reactor Physics" (28 April - 2 May 1992).

**11. CONTENTS OF CODE PACKAGE**

The package is distributed on one DS/HD (1.2 or 1.44 MB) diskette.

**12. DATE OF ABSTRACT**

July 1992.

**KEYWORDS:** COMPLEX GEOMETRY; CRITICALITY CALCULATIONS;
DIFFUSION THEORY; MULTIGROUP; NEUTRON