**1. NAME AND TITLE**

DLS: Two-Dimensional Shielding Calculational System with Diffusion Theory and Line-of-Sight Method.

**2. CONTRIBUTOR**

INTERATOM, Bensberg/Koln, Federal Republic of Germany, via the OECD Nuclear Energy
Agency Data Bank, Gif-sur-Yvette, France.

**3. CODING LANGUAGE AND COMPUTER**

FORTRAN IV; CDC 6400.

**4. NATURE OF PROBLEM SOLVED**

The neutron flux is calculated in a two-dimensional reactor-shield system. Rotationally
symmetrical geometries with gaps or other cavities, which often appear in practical shielding
problems, can be investigated conveniently with DLS.

**5. METHOD OF SOLUTION**

DLS is a two-dimensional diffusion calculational system which uses the line-of-sight technique for the treatment of transport in cavities.

Within material-filled regions, diffusion theory is used, while cavities are treated using the line-of-sight method. The numerical solution of the diffusion equation is based upon balance formulae
for all volume elements containing terms for source, absorption, and leakage. At the boundary of a
cavity, the term for the entering currents used in the balance equation include the contributions of
all other elements at the boundary of the cavity which can be seen from the element considered.
These contributions are calculated with the aid of leakage factors and view factors. The leakage
factors describe the ratio between the leaving current and the flux density. Various options are
available to calculate these leakage factors. The view factors describe the probability that a neutron
leaving the cavity surface of an arbitrary volume element hits the considered volume element
directly. The calculation of the factors proceeds upon the assumption that the neutrons emitted into
the cavity will have a cosine-shaped directional distribution.

**6. RESTRICTIONS OR LIMITATIONS**

DLS is designed for r-z geometry. Only cavities with strictly rectangular cross sections can be
considered. Maximum number of: energy groups26, view factors20000, cavities5, materials15.
The sum of radial and axial mesh intervals may not exceed 170. The total mesh number is
restricted by machine size.

**7. TYPICAL RUNNING TIME**

10 to 40 minutes for practical reactor shields (26 groups).

**8. COMPUTER HARDWARE REQUIREMENTS**

DLS was designed for the CDC 6600 computer.

**9. COMPUTER SOFTWARE REQUIREMENTS**

A FORTRAN IV compiler is required.

**10. REFERENCES**

G. Gronefeld, "Program DLS," ORNL-tr-4007 (INTERATOM--Nr. 479) (May 1973).

V. H. Vossebrecker, "Two-Dimensional Shielding Calculations Using a Combination of
Diffusion Theory and Line-of-Sight Method," *Atomkernenergie* 19, Series 1, 14-16 (1972).

G. Gronefeld, "Corrections to DLS."

D. Luigs, "New System Routine RTRN," INTERATOM Notice Nr. 33.4.1.

D. Luigs, "Notice Number 33.4.1: New System Routine RTRN," INTERATOM Notice Nr. 33.34.2, (March 1971).

D. Luigs, "Change in the Required Length in Overlay Programs," INTERATOM Notice Nr. D-A378 (June 1970).

H. Baur, "System Routine LAB," INTERATOM Notice Nr. 33.205.8 (September 1971).

D. Luigs, "Variable Dimensioning under Utilization of Blank Common," INTERATOM Notice
Nr. 33.601 (August 1972).

**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**

May 1973; updated October 1978 and February 1983; reviewed January 1985.

**KEYWORDS: ** TWO-DIMENSIONS; DIFFUSION THEORY; NEUTRON; KERNEL;
COUPLED; CAVITY