**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.

**KEYWORDS: ** NEUTRON; COMPLEX GEOMETRY; TWO-DIMENSIONS; DIFFUSION
THEORY