An Improved Fokker-Planck Angular Differencing Scheme

Abstract

An analysis is performed that shows that the standard three-point difference scheme for the Fokker-Planck angular diffusion operator rigorously preserves the zeroth angular moment, but not the first moment. As a result, the scheme does not give the exact diffusion solution in the diffusion limit. This deficiency is eliminated by means of a simple modification of the scheme. The three-point structure and positivity of the original scheme are retained in the modified scheme.