Kershaw closures for linear transport equations in slab geometry II: high-order realizability-preserving discontinuous-Galerkin schemes

TL;DR

This paper extends realizability-preserving discontinuous-Galerkin schemes to high-order full-moment models using Kershaw closures, enabling efficient solutions for linear transport equations with demonstrated convergence and robustness.

Contribution

It generalizes the scheme to arbitrary order full-moment models with Kershaw closures, improving computational efficiency for linear transport equations.

Findings

High-order methods show good convergence in tests.

Kershaw closures provide a computationally cheap closure.

The scheme effectively handles non-smooth benchmark problems.

Abstract

This paper provides a generalization of the realizability-preserving discontinuous-Galerkin scheme for quadrature-based minimum-entropy models to full-moment models of arbitrary order. It is applied to the class of Kershaw closures, which are able to provide a cheap closure of the moment problem. This results in an efficient algorithm for the underlying linear transport equation. The efficiency of high-order methods is demonstrated using numerical convergence tests and non-smooth benchmark problems.