IAEA0908 GRENADE.

1. NAME OR DESIGNATION OF PROGRAM:  GRENADE.

3. DESCRIPTION OF PROGRAM OR FUNCTION

The program is designed to solve the static diffusion equation for neutrons in multidimensional problems, assuming Cartesian geometry. The program yields flux and power distribution and the effective neutron multiplication factor (Keff).

4. METHOD OF SOLUTION

GRENADE (Green's Function Nodal Algorythm for the Diffusion Equation) described in reference 1 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 defined over a node. These integral equations represent an exact (local) solution to the coupled set of one-dimensional differential 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.

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

The size of the reactor model that can be handled is limited by computer core capacity. Cartesian geometry must be used.

6. TYPICAL RUNNING TIME

On CYBER 170/720 the solution of the IAEA 2D  benchmark problem took about 9 seconds CP time.

The test cases included in this package have been executed at the NEA-DB on a CDC CYBER 830 computer. The following CPU times were required: 8.6 seconds for the 2-D benchmark problem;  455.4 seconds for the 3-D benchmark problem.

7. UNUSUAL FEATURES OF THE PROGRAM:

8. RELATED AND AUXILIARY PROGRAMS:

10. REFERENCES

- V.N. Anghel, T.A. Beu and D.I. Simionovici,
  GRENADE - A Green's Function Nodal Algorythm for the Diffusion
  Equation,
  IRNE Internal Report, to be issued.
- R.D. Lawrence and J.J. Dorning,
  Nucl. Sci. Eng., 76,218-231 (1980).

- T.A. Beu, D.I. Simionovici and V.N. Anghel:
  GRENADE User's Manual.

11. MACHINE REQUIREMENTS

About 30 Kwords for the test run with the 2D  IAEA benchmark problem (see sections 5.3 and 9). No. of bits in a word: 60.

The execution of the 2-D benchmark problem on a CDC CYBER 830 required 77,300 (octal) words; the 3-D problem required 102,000(octal) words of main storage.

13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:  NOS1P4 552/552.

NOS2.5.1 (CDC CYBER 830).

14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS:

15. NAME AND ESTABLISHMENT OF AUTHORS

         V.N. Anghel, T.A. Beu, D.I. Simionovici
         Institute for Nuclear Power Reactors
         Pitesti, P.O.B. 78
         Romania

File name	File description	Records
IAEA0908_01.001	Information file	48
IAEA0908_01.002	JCL and control information	18
IAEA0908_01.003	GRENADE source program	2633
IAEA0908_01.004	Sample problem input 1	33
IAEA0908_01.005	Sample problem input 2	199
IAEA0908_01.006	Sample problem output	1292