An Approximate $M_2$ Model for Radiative Transfer in Slab Geometry

TL;DR

This paper introduces an approximate second order $M_2$ radiative transfer model in slab geometry using a Beta distribution ansatz, providing explicit closure and maintaining hyperbolicity, with numerical results showing good agreement with the original model.

Contribution

The paper presents a novel explicit closure for the $M_2$ radiative transfer model based on a Beta distribution, simplifying computations while preserving key properties.

Findings

Model is globally hyperbolic.

Provides explicit closure close to maximum entropy.

Numerical results show good agreement with $M_2$ model.

Abstract

We propose an approximate second order maximum entropy ($M_2$) model for radiative transfer in slab geometry. The model is based on the ansatz of the specific intensity in the form of a $\Beta$-distribution. This gives us an explicit form in its closure. The closure is very close to that of the maximum entropy, thus an approximation of the $M_2$ model. We prove that the new model is globally hyperbolic, sharing most of the advantages of the maximum entropy closure. Numerical examples illustrate that it provides solutions with satisfactory agreement with the $M_2$ model.