Derivation of Asymptotic Limiting Equations for Multigroup Anisotropic-Scattering Transport Processes in Optically Thick Regimes

Abstract

Asymptotic limit methods play a crucial role in deriving macroscopic fluid equations from equations governing mesoscopic particle transport mechanics, constituting a significant research area within kinetic theory. In this paper, we present asymptotic expansions applied to the multigroup linear transport equation with a general anisotropic scattering kernel. We derive the diffusion limit for such transport equations under three different scalings. For the conventional scaling, the standard multigroup diffusion equations are derived as an asymptotic approximation to the multigroup transport equations. For the other two scalings where the scattering effect between groups is strong, new group-collapsed (monoenergetic) diffusion approximations with different coefficients depending on the form of the scaling are derived. Numerical experiments validate the prediction of the theoretical models. This paper provides a deeper understanding of the diffusion physics for the multigroup anisotropic particle transport in the optically thick regime.