Perturbed, Entropy-Based Closure for Radiative Transfer

TL;DR

This paper introduces a hierarchy of perturbed entropy-based closures for radiative transfer, adding convective and diffusive terms to improve the standard M1 model, with numerical validation showing enhanced accuracy in shock scenarios.

Contribution

The paper develops a new hierarchy of entropy-based closure models with perturbations, incorporating additional convective and diffusive terms to improve radiative transfer simulations.

Findings

Improved accuracy over standard M1 in shock cases

Numerical simulations confirm the effectiveness of the perturbed models

Realizability and positivity are maintained in simulations

Abstract

We derive a hierarchy of closures based on perturbations of well-known entropy-based closures; we therefore refer to them as perturbed entropy-based models. Our derivation reveals final equations containing an additional convective and diffusive term which are added to the flux term of the standard closure. We present numerical simulations for the simplest member of the hierarchy, the perturbed M1 or PM1 model, in one spatial dimension. Simulations are performed using a Runge-Kutta discontinuous Galerkin method with special limiters that guarantee the realizability of the moment variables and the positivity of the material temperature. Improvements to the standard M1 model are observed in cases where unphysical shocks develop in the M1 model.