First-order continuous- and discontinuous-Galerkin moment models for a linear kinetic equation: realizability-preserving splitting scheme and numerical analysis

Abstract

We derive a second-order realizability-preserving scheme for moment models for linear kinetic equations. We apply this scheme to the first-order continuous and discontinuous models in slab and three-dimensional geometry derived in a previous paper as well as the classical full-moment $M_N$ models. We provide extensive numerical analysis as well as our code to show that the new class of models can compete or even outperform the full-moment models in reasonable test cases.