An asymptotic study of the transport equation in the Fokker-Planck limit with Angular and spatial discretization

Recent analyses have shown that the Fokker-Planck (FP) equation is an asymptotic limit of the transport equation given a forward-peaked scattering kernel satisfying certain constraints. In this paper we study discretized one-dimensional transport equations in the same limit. We show that the discrete ordinates (S{sub n}) transport equation Emits to a simple discretization of the FP equation, provided the scattering term is handled in a certain way. We also show that the linear-discontinuous (LD) and linear-moments (LM) spatial discretizations of the S, equations limit to an LD discretization of the FP equation, given the same provision about the scattering term. This provides a theoretical foundation for the application of S{sub n} methods to certain problems with forward-peaked scattering.