Some extensions of the $\phi$-divergence moment closures for the radiative transfer equation

TL;DR

This paper explores various extensions of the $\phi$-divergence moment closures for the radiative transfer equation, focusing on their approximation properties and numerical advantages over entropy-based methods.

Contribution

It introduces new variants of $\phi$-divergence closures based on different exponential and Planck function approximations, enhancing numerical stability and accuracy.

Findings

Improved conditioning of discrete equations

Exact quadrature rules preserve physical invariants

Comparative analysis of closure variants in benchmarks

Abstract

The $\phi$-divergence-based moment method was recently introduced Abdelmalik et al. (2023) for the discretization of the radiative transfer equation. At the continuous level, this method is very close to the entropy-based MN methods and possesses its main properties, i.e. entropy dissipation, rotational invariance and energy conservation. However, the $\phi$-divergence based moment systems are easier to resolve numerically due to the improved conditioning of the discrete equations. Moreover, exact quadrature rules can be used to compute moments of the distribution function, which enables the preservation of energy conservation, entropy dissipation and rotational invariants, discretely. In this paper we consider different variants of the $\phi$-divergence closures that are based on different approximations of the exponential function and the Planck function. We compare the approximation properties of the proposed closures in the numerical benchmarks.