**1. NAME AND TITLE**

EXTREME: Two-Dimensional Discrete-Ordinates Code System with Exponential Expansion
of Spatial Variables.

**2. CONTRIBUTORS**

University of Tennessee, Department of Nuclear Engineering, Knoxville, Tennessee.

Oak Ridge National Laboratory, Oak Ridge, Tennessee.

**3. CODING LANGUAGE AND COMPUTER**

Fortran IV; IBM 3033.

**4. NATURE OF PROBLEM SOLVED.**

EXTREME was designed for use in the development and testing of a new family of methods for
the calculation of spatial dependence of neutron density in nuclear systems in two-dimensional
Cartesian geometry. The computer code system is designed to handle an arbitrary number of spatial,
energy, and angle subdivisions. Any degree of scattering anisotropy can be handled for either external
source or fission systems.

**5. METHOD OF SOLUTION**

The basic approach is to (1) approximate the spatial variation of the neutron source across each
spatial subdivision as an expansion in terms of a user-supplied set of exponential basis functions;
(2) solve analytically for the resulting neutron density inside each region; and (3) approximate this
density in the basis function space in order to calculate the next iteration flux-dependent source terms.
In the general case the calculation is iterative due to neutron sources which depend on the neutron
density itself.

**6. RESTRICTIONS OR LIMITATIONS**

EXTREME is designed to handle only Cartesian x-y geometry. It is required that the weights sum
to one and that necessary reflection angles are present at reflection boundaries; if either of these is not
met, the code will so indicate and stop.

**7. TYPICAL RUNNING TIME**

On the IBM 3033, the sample problem used 2 minutes and 15.29 CPU seconds.

**8. COMPUTER HARDWARE REQUIREMENTS**

EXTREME is operable on the IBM 3033.

**9. COMPUTER SOFTWARE REQUIREMENTS**

A Fortran IV compiler is required.

**10. REFERENCE**

R. E. Pevey, "Development of a New Two-Dimensional Cartesian Geometry Nodal Multigroup
Discrete Ordinates Method," ORNL/CSD/TM-182 (July 1982).

**11. CONTENTS OF CODE PACKAGE**

Included are the referenced document and one (1.2MB) DOS diskette which contains the job
control language used locally for execution, the source code plus sample problem input and output.

**12. DATE OF ABSTRACT**

December 1983.

**KEYWORDS: ** DISCRETE ORDINATES; MULTIGROUP; TWO-DIMENSIONS; NEUTRON