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We derive a second-order realizability-preserving scheme for moment modelsfor linear kinetic equations. We apply this scheme to the first-ordercontinuous and discontinuous models in slab and three-dimensional geometryderived 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 thenew class of models can compete or even outperform the full-moment models inreasonable test cases.

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