Determination of the expansion coefficients of a 1-D multigroup diffusion nodal model

Abstract

This paper describes the determination of the unknown polynomial expansion coefficients in a diffusion theory nodal model. The expansion coefficients are determined from a linear system of equations using the source iteration technique. The Gaussian elimination method, consisting of the forward elimination and the backward substitution processes is used to solve the system of equations. Using the method described in this paper, application of the forward elimination process is only necessary at the first iteration, provided that the material properties and/or the geometry of the problem remain constant. As a result, the number of calculations required to determine the unknown polynomial coefficients, using the Gaussian elimination process, can be decreased. This method is especially advantageous in multidimensional nodal models and when high orders of the polynomial expansion are used.