** **

**1. NAME AND TITLE**

KASY**: **3-D Homogeneous Neutron Diffusion in
X-Y-Z, R-Theta, Hexagonal-Z Geometry by Synthesis Method.

**2. CONTRIBUTOR**

Institut
fur Neutronenphysik and Reaktortechnik, Kernforschungszentrum Karlsruhe, Germany
through the OECD Nuclear Energy Agency Data Bank, Issy-les-Moulineaux, France.

**3. CODING LANGUAGE
AND COMPUTER**

Fortran IV; IBM 370 Series (C00814I037000).

**4. NATURE OF
PROBLEM SOLVED**

The multigroup neutron diffusion equations are solved for three-dimensional x-y-z, r-theta-z and hexagonal-z geometries in the homogeneous case. KASY calculates the three-dimensional flux-distribution and also the eigenvalue, Keff. Only downscattering of neutrons is allowed.

**5. METHOD OF
SOLUTION**

KASY solves the three dimensional multigroup diffusion equations by means of a synthesis method using available two-dimensional trial-functions. The method of solution is based on the variational method of Kantorovich and developed by Kaplan. Before use, the trial-functions are orthonormalized for better convergence of the variational process.

a) Four outer boundary conditions may be imposed - zero flux, zero current or constant current/flux at the upper and lower boundaries. Boundaries must be fulfilled by the trial-functions.

b) Scattering down from any energy-group to any other is allowed.

c) There are several possibilities in KASY to:

· Separate distinct trial-functions out of a file which contains a series of precalculated two-dimensional functions.

· Make group-collapsing of precalculated trial-functions by means of group-flux addition.

· Orthonormalize the precalculated trial-functions to get a better convergence.

**6. RESTRICTIONS OR
LIMITATIONS**

The maximum number of mesh points is 150 in each space-direction and the maximum number of trial functions is 8 (no blending technique is used). It is expected, that for the orthonormalization all two-dimensional trial functions for all energy groups have to be in core storage at the same time. This means the working space in core-storage must be k.mxn.ngp storage words, where k is the number of two-dimensional trial-functions; mxn, the number of mesh points in these two dimensions and ngp is the number of energy-groups. Within this range, KASY uses core storage and turns automatically to external storage devices, when there is no more free space. (In such cases, these external devices must be defined. For the list of possible external devices, see input description.)

**7. TYPICAL RUNNING
TIME**

It is estimated, that one synthesis calculation takes the same running time, as is needed for calculating one two-dimensional trial-function. This statement is approximately independent of the number of mesh-points and trial-functions.

**8. COMPUTER
HARDWARE REQUIREMENTS**

The minimum extension of core storage, which KASY uses, is the sum of the number of storage words for the machine instructions of the program (15000 at the moment by use of overlay structure), extension of the working space and the extensions of buffers for I/O operations. In this range KASY can be adapted to the given installation.

**9. COMPUTER
SOFTWARE REQUIREMENTS**

Standard IBM OS MVT

**10. REFERENCES**

**a) Included Documentation**

G. Buckel: “Approximation of the Stationary Three-Dimensional Neutron Diffusion Equation by a Synthesis Method with the Karlsruhe Synthesis Program KASY,” KFK 1349 (June 1971)(in German).

S. Pilate E.A.: “A Three Dimensional Synthesis Method Tested and Applied in Fast Breeders,” KFK 1345 (August 1971).

**11. CONTENTS OF CODE
PACKAGE**

The package is distributed on a CD with a compressed zip file including source files, JCL, documentation and sample data and output.

**12. DATE OF ABSTRACT**

November 2013.

**KEYWORDS**: BREEDING,
DIFFUSION EQUATIONS, FAST REACTORS, HOMOGENEOUS REACTORS, MULTIGROUP, R-THETA-Z,
SYNTHESIS, THREE-DIMENSIONAL, X-Y-Z