A composite spatial grid spectral Green's function method for one speed discrete ordinates eigenvalue problems in two-dimensional Cartesian geometry

Abstract

Spectral Green's function nodal methods (SGF) are well established as a class of coarse mesh methods. For this reason, they are widely used in the solution of neutron transport problems in discrete ordinates formulation (SN). When compared with fine mesh methods, SGF are considered efficient, as solutions are as accurate as, using a smaller number of spatial nodes, reducing floating point operations. However, the development of spectral-nodal methods for XY Cartesian geometries, has been limited due to (a) difficulties in implementing efficient computational algorithms and, (b) high algebraic and computational costs. This is because these methods need to use NBI-type (One-Node Block Inversion) sweep schemes. The composite spatial grid methods were developed to overcome these challenges. In this work, we describe a composite spatial grid spectral-nodal method to solve one-speed discrete ordinate eigenvalue problems in XY Cartesian geometry with isotropic scattering. The discretization is developed into two stages and two 1D problems coupled by transverse leakage terms in each domain region are obtained. In order to converge toward the numerical solution, we used an alternating-direction iterative technique and a modified source iteration sweep scheme. Also, we used the conventional power method to estimate the problem's dominant eigenvalue. Numerical results for benchmark problems are presented to illustrate the accuracy and performance of the developed method. This approach offers more accurate and efficient results for integral quantities if compared with others SGF methods.