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

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.

References in corpus (2)

• A realizability-preserving discontinuous Galerkin scheme for entropy-based moment closures for linear kinetic equations in one space dimension
• A realizability-preserving high-order kinetic scheme using WENO reconstruction for entropy-based moment closures of linear kinetic equations in slab geometry

Cited by in corpus (7)

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