标题： 二阶矩方法在热辐射传输中的对比研究 显示英文标题

标题： A Comparison of the Consistent and Independent Second Moment Methods Applied to Thermal Radiative Transfer

摘要： 高效数值方法的设计对于模拟热辐射传输（TRT）具有挑战性，因为辐射与物质能量之间的刚性非线性耦合，尤其是在高能量密度物理和天体物理学中感兴趣的时间尺度上。 在这里，我们研究了二阶矩方法（SMM）在多群离散坐标输运方程中的吸收-发射加速应用，该方程采用间断伽辽金空间离散化。 SMM采用了一种基于降低维度的扩散模型来描述辐射传输，当与适当的离散闭合耦合时，可以作为输运方程的代理，从而将输运方程从刚性的吸收-发射物理中隔离出来。 我们使用灰度低阶系统来降低求解低阶系统的成本，并利用专门为可扩展求解现有线性求解器技术而设计的SMM低阶离散化。 我们的算法稳健地解决了非线性TRT系统，仅依赖于输运扫描、线性求解对称且正定的灰度扩散系统以及非线性求解空间点能量平衡方程。 该算法被用作一种工具，以比较为一维和二维稳态线性输运问题中灰度和多群TRT问题开发的低阶离散化的有效性。 显示英文摘要

摘要： The design of efficient numerical methods for modeling thermal radiative transfer (TRT) is challenging due to the stiff, nonlinear coupling between radiation and material energies, especially at the time scales of interest in high energy density physics and astrophysics. Here, we investigate the use of the Second Moment Method (SMM) to accelerate absorption-emission within the context of the multigroup, Discrete Ordinates transport equations with discontinuous Galerkin spatial discretization. SMM employs a reduced-dimensional, diffusion-based model of radiation transport that, when coupled with suitable discrete closures, serves as a proxy for the transport equation, isolating the transport equation from the stiff absorption-emission physics. We use a gray low-order system to reduce the cost of solving the low-order system and leverage SMM low-order discretizations specifically designed to be scalably solvable with existing linear solver technology. Our algorithm robustly resolves the nonlinear TRT system while only relying on transport sweeps, linearly solving symmetric and positive definite, gray diffusion systems, and nonlinearly solving the spatially pointwise energy balance equation. This algorithm is used as a vehicle to compare the efficacy of low-order discretizations developed for steady-state, linear transport on gray and multigroup TRT problems in one and two spatial dimensions.