1. NAME AND TITLE

SHADOK: Transport Code Systems, P1 Scattering in Infinite Cylindrical and Spherical Geometries by Polynomial Approximation.

AUXILIARY ROUTINES

SHADOK3: Cylindrical geometry, direct solution of the linear system.

SHADOK4: Cylindrical geometry, thermalization iteration, solution of the linear system with inverse matrix calculation.

SHADOK5: Like SHADOK3 for spherical geometry.

SHADOK6: Like SHADOK4 for spherical geometry.

2. CONTRIBUTOR

Federal Institute for Reactor Research (EIR), Wurenlingen, Switzerland, through the OECD NEA Data Bank, Gif-sur-Yvette, France.

3. CODING LANGUAGE AND COMPUTER

FORTRAN IV and COMPASS; CDC 6600.

4. NATURE OF PROBLEM SOLVED

The SHADOK series was designed to solve the integral transport equation with P₁ scattering in infinite cylindrical and spherical geometries by polynomial approximation.

5. METHOD OF SOLUTION

The cylindrical transport medium composed of one or more materials is divided into annular rings. In each ring, the flux and isotropic sources are expanded spatially in a four-term Legendre polynomial series. Similarly, the current and anisotropic sources are expanded in a three-term series. The coefficients of the Legendre polynomials can be related to the first and second spatial moments of the flux and the boundary fluxes. When these expansions are introduced into the integral transport equation, a matrix equation results. This equation is then solved to yield the boundary flux, first moment of the flux and second moment of the flux.

6. RESTRICTIONS OR LIMITATIONS

None noted.

7. TYPICAL RUNNING TIME

No study was made by RSIC of typical running times for SHADOK.

8. COMPUTER HARDWARE REQUIREMENTS

SHADOK is operable on the CDC 6600 computer.

9. COMPUTER SOFTWARE REQUIREMENTS

A FORTRAN IV compiler is required. Two subroutines are in mixed mode.

10. REFERENCES

J. Ligou, P. Thomi, "Codes for Solving the Integral Transport Equation with P1 Scattering in Infinite Cylindrical and Spherical Geometries by Polynomial Approximation," TM-PH-454 (August 1973).

J. Ligou, "Improved Integral Transport Theory by Means of Space Polynomial Approximations," Nucl. Sci. Eng. 50, 135-146 (1973).

11. CONTENTS OF CODE PACKAGE

Included are the referenced documents and one (1.2MB) DOS diskette which contains the source code and sample problem input and output.

12. DATE OF ABSTRACT

July 1973; updated July 1975.