An asymptitic analysis of the fokker-planck limit of a general spatial moment method for the transport equation

Abstract

An asymptotic analysis of the spatially discretized particle transport equation in the Fokker-Planck limit is performed. This asymptotic limit corresponds to particle transport in medium with highly forward-peaked scattering. A general spatial moment (GSM) method is analyzed. It defines a family of spatial discretization methods. The GSM method is based on a set of spatial moments of the transport equation and linear auxiliary equations with coefficients that nonlinearly depend on cross sections. A majority of existing discretization schemes for the transport equation belongs to the group of such methods. The general conditions, under which the considered family of methods satisfies the Fokker-Planck asymptotic limit, are derived. The characteristic methods are studied. The analysis gives an insight into the asymptotic properties of a broad group of transport discretization methods.