1. NAME AND TITLE

GRENADE: Green's Function Nodal Algorithm for the Diffusion Equation.

2. CONTRIBUTORS

Institute for Nuclear Power Reactors, Pitesti, Romania.

ECS Power Systems Inc., Ottawa, Canada.

3. CODING LANGUAGE AND COMPUTER

Fortran; CDC Cyber 170/720 (A) and VAX (B).

4. NATURE OF PROBLEM SOLVED

GRENADE is a coarse-mesh program designed for neutronic flux and power calculations in nuclear reactors. It solves the static diffusion equation for neutrons in multidimensional problems, assuming Cartesian Geometry. The program yields flux and power distributions and the effective neutron multiplication factor .

5. METHOD OF SOLUTION

"Green's Function Nodal Algorithm for the Diffusion Equation" (GRENADE), described in Ref. 2 below, is based on the linear form of the nodal balance equation written in terms of the average net interface currents across the surface of a subdomain (node). Green's functions for the one-dimensional in-group diffusion-removal operators are used to generate a coupled set of one-dimensional integral equations obtained by spatially integrating the multidimensional diffusion equation over directions transverse to each coordinate direction.

The integral equations are approximated using a weighted residual procedure. The resulting matrix equations, when solved in conjunction with the linear form of the nodal balance equations, provide the necessary additional relationships between the net interface currents and the flux within the node.

6. RESTRICTIONS OR LIMITATIONS

The size of the reactor model that can be handled is limited by computer core capacity. Cartesian geometry must be used. The VAX version is limited by the working-set-extent (amount of virtual memory available.)

7. TYPICAL RUNNING TIME

On the CYBER 170/720 the solution of the IAEA 2D benchmark problem took about 9 seconds CP time. The test case executes in 30 seconds on a MICROVAX-II.

8. COMPUTER HARDWARE REQUIREMENTS

About 30 K words storage was required to run the two-dimensional IAEA benchwork sample problem (file 2 of Version A). The VAX version was converted to run on a MICROVAX-II and was tested by RSIC on a VAX 11/780.

9. COMPUTER SOFTWARE REQUIREMENTS

The Cyber version executes under the NOS1P4 552/552 operating system. A Fortran IV compiler is required. The VAX version runs under VMS.

10. REFERENCES

a. Included in package:

T. A. Beu, D. I. Simionovici and V. N. Anghel "GRENADE User's Manual" Informal Report (1985).

b. Background information:

V. N. Anghel, T. A. Beu and D. I. Simionovici, "GRENADE - A Green's Function Nodal Algorithm for the Diffusion Equation," IRNE Internal Report, to be issued.

R. D. Lawrence and J. J. Dorning, Nucl. Sci. Eng., 76, 218-231 (1980).

11. CONTENTS OF CODE PACKAGE

Included are the referenced document and one (1.2MB) DOS diskette containing the source code and sample problem input.

12. DATE OF ABSTRACT

September 1987, updated December 1989.