Recent Advances in Spectral Nodal Methods for Numerically Solving Neutron‐Diffusion Eigenvalue Problems

Abstract

In this paper we present the recent advances in spectral nodal methods for numerically solving neutron-diffusion eigenvalue problems in Cartesian geometry. For one‐dimensional two‐energy group diffusion criticality problems, we describe the use of nonconventional albedo boundary conditions that substitute approximately the reflective properties of the nonmultiplying media around the core. We also present the Chebyshev acceleration scheme for the power method used in the outer iterations. For three‐dimensional one‐speed diffusion eigenvalue problems, we present a spectral nodal method that is based on transverse‐integrating the diffusion equation separately in X, Y, and Z directions, and then considering flat approximations for the transverse leakage terms. Numerical results for typical model problems are given to illustrate the accuracy.

Acknowledgments

The authors note the support of Conselho Nacional de Desenvolvimento Cientifico e Tecnológico (CNPq‐Brazil) and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES‐Brazil) for the development of this work.