Finite Difference Solution for Multigroup Transport Equation in r-z Geometry by Spherical Harmonics Method

Abstract

In the r-z geometry, a second order differential equation for spherical harmonics moments is derived, and for simplicity, it includes only higher order of scattering within a group Using the finite difference approximation for this spherical harmonics equation, a multi-group transport code of a general order of approximation is developed. Sample calculations are carried out for external source problem in pure absorber, Gelberd's benchmark shielding problem of two groups, four groups criticality problem of fast reactor, and the results were compared with exact solution based on analytic method or with those obtained by discrete-ordinates method It is shown that the present method gives more accurate results than the discrete-ordinates method in the reasonable computation time for shielding problems of the strong absorber because of the disappearance of the ray effect, although this spherical harmonics code requires more computer memory than the discrete-ordinates method