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.
A strong second-order two-stage explicit/implicit technique with spectral orthogonal basis Galerkin finite element method for two-dimensional Gray-Scott model
Imam Mohammad Ibn Saud Islamic University (IMSIU)（伊玛目穆罕默德·伊本·沙特伊斯兰大学）
Differentiate the Solver, Not the Equation: Reverse-Sweep Adjoints for Block Implicit Simulation
Stanford University（斯坦福大学）；University of California, Los Angeles（加州大学洛杉矶分校）；LightSpeed Studios, Tencent America（腾讯美国光速工作室）；The University of Utah（犹他大学）
Compact difference schemes for weakly-nonlinear parabolic and Schrodinger-type equations and systems
National Research University Higher School of Economics（国立高等经济大学）；Hydrometeorological Center of Russia（俄罗斯水文气象中心）；Skolkovo Institute for Science and Technology（斯科尔科沃科学技术学院）
Jülich Supercomputing Centre, Forschungszentrum Jülich GmbH（于利希超级计算中心，于利希研究中心有限公司）；Institute of Computational Science, Università della Svizzera italiana（意大利瑞士大学计算科学研究所）；Institute for Computational and Mathematical Engineering, Stanford University（斯坦福大学计算与数学工程研究所）；Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室计算科学与工程中心）
Jülich Supercomputing Centre, Forschungszentrum Jülich（于利希超级计算中心，于利希研究中心）；Institute of Computational Science, Università della Svizzera italiana（瑞士意大利语大学计算科学研究所）；Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室计算科学与工程中心）；Institute for Computational and Mathematical Engineering, Stanford University（斯坦福大学计算与数学工程研究所）；Department of Mathematics, Bergische Universität Wuppertal（伍珀塔尔山岳大学数学系）
