A scheme for the evaluation of dominant time-eigenvalues of a nuclear reactor

This paper presents a scheme to obtain the fundamental and few dominant solutions of the prompt time eigenvalue problem (referred to as alpha-eigenvalue problem) for a nuclear reactor using multi-group neutron diffusion theory. The scheme is based on the use of an algorithm called Orthomin(l). This algorithm was originally proposed by Suetomi and Sekimoto [Suetomi, E., Sekimoto, H., 1991. Conjugate gradient like methods and their application to eigenvalue problems for neutron diffusion equations. Ann. Nucl. Energy IS (4), 205-227] to obtain the fundamental K-eigenvalue (K-effective) of nuclear reactors. Recently, it has been shown that the algorithm can be used to obtain the further dominant K-modes also. Since alpha-eigenvalue problem is Usually more difficult to solve than the K-eigenvalue problem, an attempt has been made here to use Orthomin( I) for its solution. Numerical results are given for realistic 3-D test case. (c) 2007 Elsevier Ltd. All rights reserved.