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 α-eigenvalue problem) for a nuclear reactor using multi-group neutron diffusion theory. The scheme is based on the use of an algorithm called Orthomin(1). 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 18 (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 α-eigenvalue problem is usually more difficult to solve than the K-eigenvalue problem, an attempt has been made here to use Orthomin(1) for its solution. Numerical results are given for realistic 3-D test case.