Solution of K-eigenvalue problem by nodal diffusion method using Orthomin(l) algorithm

摘要

This paper deals with the use of Orthomin(l) algorithm for the solution of K-eigenvalue problem in multi-group neutron diffusion theory in a code based on nodal expansion method (NEM). The fundamental K-eigenvalue is usually obtained by power iteration method. There exists another quite efficient but not so well-known approach based on Orthomin(l) algorithm, initially proposed by Suetomi and Sekimoto [1991, Conjugate gradient like methods and their application to eigenvalue problems for neutron diffusion equations, Annals of Nuclear Energy, 18(4), 205-227] to find fundamental mode solution of K-eigenvalue problem. For finite differenced diffusion equation, it has been shown recently that if the algorithm is applied to the K-eigenvalue equation cast in terms of fission matrix, it can be implemented by making few changes in conventional power iteration codes. Here the algorithm is implemented in a similar way for the NEM. The Orthomin(l) algorithm can be used to find higher harmonics by simply changing the initial flux guess. Numerical results are given for 2-D and 3-D IAEA PWR benchmark problems.