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.

翻译：热辐射传递领域的基准解集在某些方面存在覆盖缺口，特别是非线性非平衡问题。此外，目前尚无非平衡光学厚基准解。这些不足促使我们开发了一种无需线性假设、且能轻松收敛于光滑光学厚问题的数值方法——采用未碰撞源处理的移动网格间断伽辽金（DG）框架。鉴于该方法已在含时散射输运问题中得到验证，本文针对熟悉线性化系统及更具物理意义的非线性系统，在光学薄与光学厚两种区域中，给出了非平衡热辐射传递问题的解，涵盖全输运及$S_2$/$P_1$解。对于光滑源项，在所有时刻均观察到几何收敛；而对于非光滑源项，在局部平衡条件下后期亦呈现几何收敛。此外，当解不光滑时，阶跃源项问题仍可获得精确解。