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

## TL;DR

This paper develops a second-order, realizability-preserving numerical scheme for first-order continuous and discontinuous Galerkin moment models of linear kinetic equations, demonstrating competitive performance against classical full-moment models.

## Contribution

It introduces a novel second-order splitting scheme that preserves realizability for first-order Galerkin moment models, with extensive numerical validation.

## Key findings

- The new scheme maintains realizability in simulations.
- The models can outperform classical full-moment models in test cases.
- Numerical analysis confirms the effectiveness of the approach.

## 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.