Benchmark solutions for radiative transfer with a moving mesh and exact uncollided source treatments

TL;DR

This paper develops benchmark solutions for thermal radiative transfer problems, addressing gaps in existing benchmarks, especially for nonlinear and non-equilibrium scenarios, using a novel moving mesh DG method with uncollided source treatment.

Contribution

The paper introduces a moving mesh Discontinuous Galerkin framework capable of accurately solving nonlinear, non-equilibrium radiative transfer problems in both optically thick and thin regimes.

Findings

Geometric convergence observed for smooth sources at all times.

Accurate solutions achieved for step sources with nonsmooth initial conditions.

Method successfully applied to both linearized and nonlinear systems.

Abstract

The set of benchmark solutions used in the thermal radiative transfer community suffer some coverage gaps, in particular nonlinear, non-equilibrium problems. Also, there are no non-equilibrium, optically thick benchmarks. These shortcomings motivated the development of a numerical method free from the requirement of linearity and easily able to converge on smooth optically thick problems, a moving mesh Discontinuous Galerkin (DG) framework that utilizes an uncollided source treatment. Having already proven this method on time dependent scattering transport problems, we present here solutions to non-equilibrium thermal radiative transfer problems for familiar linearized systems together with more physical nonlinear systems in both optically thin and thick regimes, including both the full transport and the $S_2$/$P_1$ solution. Geometric convergence is observed for smooth sources at all times and some nonsmooth sources at late times when there is local equilibrium. Also, accurate solutions are achieved for step sources when the solution is not smooth.