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NEA-0343 KASY.

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

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1. NAME OR DESIGNATION OF PROGRAM:  KASY.
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2. COMPUTERS
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Program name Package id Status Status date
KASY NEA-0343/01 Tested 01-NOV-1972

Machines used:

Package ID Orig. computer Test computer
NEA-0343/01 IBM 370 series IBM 370 series
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3. NATURE OF PHYSICAL 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.
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4. 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.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

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.)
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6. 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.
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7. UNUSUAL FEATURES OF THE PROGRAM

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.
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8. RELATED AND AUXILIARY PROGRAMS

KASY will soon be incorporated into  the new Karlsruhe nuclear programme system KAPROS. KAPROS will also  soon include another newly designed programme AUDI3, which will contain evaluation routines for reaction rates, densities, prompt and delayed neutron lifetimes, as well as a three dimensional perturbation part.
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9. STATUS
Package ID Status date Status
NEA-0343/01 01-NOV-1972 Tested at NEADB
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10. REFERENCES

- 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).
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11. MACHINE 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 programme (15000 at the moment by use of overlay structure), extension of the working space (see point 5 of this abstract) and the extensions of buffers for I/O operations.
In this range KASY can be adapted to the given installation.
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
NEA-0343/01 FORTRAN-IV
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13. OPERATING SYSTEM OR MONITOR UNDER WHICH PROGRAM IS EXECUTED:  Standard IBM OS MVT.
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14. ANY OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

It is possible to give KASY the extension of the working space in the core storage in bytes (see point 5 of this abstract) by means of the parameter PARM.G of the EXEC-statement of the IBM 360 OS job-control-language.
Geometries may be calculated by the computer programme DIXY.
KASY contains a routine which gives the printout of the input description and also the error-listing. It can be obtained when the  extension of the above mentioned working space in the PARM.G parameter is greater than the REGION.G parameter in the EXEC-statement of the IBM 360 OS job-control-language.
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15. NAME AND ESTABLISHMENT OF AUTHOR

      G. Buckel
      Kernforschungszentrum
      Karlsruhe, Germany
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16. MATERIAL AVAILABLE
NEA-0343/01
File name File description Records
NEA0343_01.001 INFORMATION 6
NEA0343_01.002 KASY SOURCE PROGRAM 3939
NEA0343_01.003 AGABE SOURCE PROGRAM 1009
NEA0343_01.004 DIXY SAMPLE INPUT DATA 199
NEA0343_01.005 KASY JCL+OVERLAY CARDS+SAMPLE INPUT DATA 301
NEA0343_01.006 AGABE JCL+OVERLAY CARDS+SAMPLE INPUT DATA 24
NEA0343_01.007 DIXY SAMPLE PROBLEM PRINTED OUTPUT 1515
NEA0343_01.008 KASY SAMPLE PROBLEM PRINTED OUTPUT 483
NEA0343_01.009 AGABE SAMPLE PROBLEM PRINTED OUTPUT 5455
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17. CATEGORIES
  • C. Static Design Studies

Keywords: breeding, diffusion equations, fast reactors, homogeneous reactors, multigroup, r-theta-z, synthesis, three-dimensional, x-y-z.