**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 P_{1} 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.

**KEYWORDS: ** INTEGRAL BOLTZMANN EQUATION; POLYNOMIAL
APPROXIMATION; NEUTRON; MULTIGROUP; ONE-DIMENSION;
CYLINDRICAL GEOMETRY; SPHERICAL GEOMETRY