3D calculation of the lambda eigenvalues and eigenmodes of the two-group neutron diffusion equation by coarse-mesh nodal methods

This paper shows the development and roots of the lambda eigenvector and eigenmodes calculation by coarse-mesh finite difference nodal methods. In addition, this paper shows an inter-comparison of the eigenvalues and power profiles obtained by different 3D nodal methods with two neutron energy groups. The methods compared are: the nodal collocation method (Verdú et al., 1998, 1993; Hebert, 1987) with different orders of the Legendre expansions, the modified coarse-mesh nodal method explained in this paper, and the method implemented in the PARCS code by Wysocki et al. (2014, 2015). In this paper we have developed a program NODAL-LAMBDA that uses a two-group modified coarse-mesh finite difference method with albedo boundary conditions. Some of the approximations performed originally by Borressen (1971) have been discarded and more exact expressions have been used. We compare for instance the eigenvalues and power profiles obtained with Borressen original approach of 1.5 group and with 2 groups. Also, some improvements in the albedo boundary conditions suggested by (Turney 1975; Chung et al., 1981) have been incorporated to the code as an option. The goal is to obtain the eigenvalues and the sub-criticalities (k_i−k₀) of the harmonic modes that can be excited during an instability event in a fast way and with an acceptable precision.