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：热辐射输运（TRT）是一个与时间相关的高维偏积分-微分方程。在实际应用中，如惯性约束聚变，TRT 常与流体力学、等离子体等其他物理过程耦合，且人们通常关注的时间尺度远慢于辐射时间尺度。因此，TRT 通常采用隐式方法处理；由于其刚性和高维特性，它在多物理场模拟中往往是主要的计算成本来源。本文在确定性 S$_N$ 框架下，为灰体 TRT 的隐式-显式（IMEX）积分提出了一种新方法，该方法每阶段仅需一次扫描，最简单的一阶方法每个时间步仅需一次扫描。方程的划分通过基于矩的高阶-低阶 TRT 公式实现，其中利用输运算子及其前两个矩来捕捉输运极限和扩散极限的渐近刚性区域。吸收-再发射过程采用显式处理，尽管具有刚性，但通过隐式求解已得到充分阻尼，使得我们无需将高阶与低阶方程隐式耦合，即可实现稳定、精确的时间积分。由于高阶与低阶方程通过温度相关的不透明度存在非线性耦合，为便于 IMEX 划分及高阶方法的应用，我们采用了一种适用于非线性划分的半隐式积分方法。通过在厚 Marshak 和弯曲管道基准问题上展示结果，该方法在精度和实际计算时间方面，相比通常使用的标准一阶隐式积分，取得了数量级的改进。