Kershaw closures for linear transport equations in slab geometry I: model derivation

TL;DR

This paper introduces a new class of computationally efficient moment models for linear kinetic equations in slab geometry that maintain the crucial non-negativity property, offering a promising alternative to more costly minimum-entropy models.

Contribution

The paper develops a novel Kershaw closure method for linear transport equations that is both computationally cheap and preserves realizability, matching the approximation quality of existing models.

Findings

Models are computationally efficient.

Models preserve non-negativity (realizability).

Comparable approximation quality to minimum-entropy models.

Abstract

This paper provides a new class of moment models for linear kinetic equations in slab geometry. These models can be evaluated cheaply while preserving the important realizability property, that is the fact that the underlying closure is non-negative. Several comparisons with the (expensive) state-of-the-art minimum-entropy models are made, showing the similarity in approximation quality of the two classes.