Thermal radiation transport (TRT) is a time dependent, high dimensional partial integro-differential equation. In practical applications such as inertial confinement fusion, TRT is coupled to other physics such as hydrodynamics, plasmas, etc., and the timescales one is interested in capturing are often much slower than the radiation timescale. As a result, TRT is treated implicitly, and due to its stiffness and high dimensionality, is often a dominant computational cost in multiphysics simulations. Here we develop a new approach for implicit-explicit (IMEX) integration of gray TRT in the deterministic S$_N$ setting, which requires only one sweep per stage, with the simplest first-order method requiring only one sweep per time step. The partitioning of equations is done via a moment-based high-order low-order formulation of TRT, where the streaming operator and first two moments are used to capture the asymptotic stiff regimes of the streaming limit and diffusion limit. Absorption-reemission is treated explicitly, and although stiff, is sufficiently damped by the implicit solve that we achieve stable accurate time integration without incorporating the coupling of the high order and low order equations implicitly. Due to nonlinear coupling of the high-order and low-order equations through temperature-dependent opacities, to facilitate IMEX partitioning and higher-order methods, we use a semi-implicit integration approach amenable to nonlinear partitions. Results are demonstrated on thick Marshak and crooked pipe benchmark problems, demonstrating orders of magnitude improvement in accuracy and wallclock compared with the standard first-order implicit integration typically used.

翻译：热辐射传输（TRT）是一类含时高维偏积分微分方程。在惯性约束聚变等实际应用中，TRT与流体力学、等离子体等其他物理过程耦合，且人们关注的物理时间尺度通常远大于辐射时间尺度。因此，TRT通常采用隐式处理，而由于其刚性特性和高维特征，它在多物理场模拟中往往占据主导计算成本。本文针对确定论S$_N$框架下的灰体TRT提出一种新型隐式-显式（IMEX）积分方法，每阶段仅需一次扫描，其中最简单的一阶方法每时间步仅需一次扫描。方程的分割基于TRT的高阶-低阶矩格式，利用输运算子与前两阶矩捕捉输运极限和扩散极限的渐进刚性区域。吸收-再发射过程采用显式处理，尽管其具有刚性，但通过隐式求解的充分阻尼，我们无需将高阶与低阶方程隐含耦合即可实现稳定精确的时间积分。针对高阶与低阶方程通过温度相关不透明度产生的非线性耦合，为便于IMEX分割并实现高阶方法，我们采用适用于非线性分割的半隐式积分方法。通过厚Marshak与弯曲管道基准问题的数值验证，所提方法相比标准一阶隐式积分，在精度与计算耗时方面均实现数量级改善。