NUMERICAL SOLUTION OF THE NEUTRON DIFFUSION EQUATION

Abstract

7 I. DESCRIPTION OF THE PROBLEM 9 A. Introduction 9 B. Statement of Objectives 11 C. The Multigroup Formalism and the Power Iteration Method . . . 11 II. FORMULATION OF A GALERKIN-TYPE APPROXIMATION PROCEDURE 16 A. Introduction 16 B. Statement of the Problem and Properties of the Solution . . . 18 C. The Galerkin Approximation Procedure 25 III. SOLUTION OF THE APPROXIMATE PROBLEM 32 A. Choice of a Finite-dimensional Subspace 32 B. Construction of a Basis 33 C. Solution of the Approximate Problem 38 D. Generation of the Coefficients 39 IV. DESCRIPTION OF THE RESEARCH COMPUTER PROGRAM HOD 46 V. A TIMING COMPARISON STUDY 48 A. Introduction 48 B. Description of the Computer Program DARC2D 48 C. Scope and Limitations of the Studies 50 D. A Homogeneous Reactor Configuration 54 E. A Simple Two-zone Reactor Configuration 62 F. A 1,000 MWe Liquid Metal Fast Breeder Reactor Configuration . 72 G. A Loosely Coupled Reactor Configuration 78 H. Conclusions 92 VI. SUMMARY AND CONCLUSIONS 95 APPENDIX 96 ACKNOWLEDGEMENT 97 REFERENCES 98