A new variable Eddington factor (VEF) model is presented for nonlinear problems of thermal radiative transfer (TRT). The VEF model is a data-driven one that acts on known (a-priori) radiation-diffusion solutions for material temperatures in the TRT problem. A linear auxiliary problem is constructed for the radiative transfer equation (RTE) with opacities and emission source evaluated at the known material temperatures. The solution to this RTE approximates the specific intensity distribution for the problem in all phase-space and time. It is applied as a shape function to define the Eddington tensor for the presented VEF model. The shape function computed via the auxiliary RTE problem will capture some degree of transport effects within the TRT problem. The VEF moment equations closed with this approximate Eddington tensor will thus carry with them these captured transport effects. In this study, the temperature data comes from multigroup $P_1$, $P_{1/3}$, and flux-limited diffusion radiative transfer (RT) models. The proposed VEF model can be interpreted as a transport-corrected diffusion reduced-order model. Numerical results are presented on the Fleck-Cummings test problem which models a supersonic wavefront of radiation. The presented VEF model is shown to reliably improve accuracy by 1-2 orders of magnitude compared to the considered radiation-diffusion model solutions to the TRT problem.

翻译：针对热辐射传输（TRT）的非线性问题，提出了一种新型可变爱丁顿因子（VEF）模型。该VEF模型是基于数据驱动的，作用于已知的（先验）TRT问题中材料温度辐射-扩散解。针对辐射传输方程（RTE），构建了一个线性辅助问题，其中不透明度与发射源基于已知材料温度进行评估。该RTE的解近似于整个相空间与时间中问题的特定强度分布，并作为形状函数用于定义所提出VEF模型的Eddington张量。通过辅助RTE问题计算的形状函数能够捕获TRT问题中一定程度的输运效应。利用此近似Eddington张量闭合的VEF矩方程将继承这些被捕获的输运效应。本研究中，温度数据来自多群$P_1$、$P_{1/3}$及通量限扩散辐射传输（RT）模型。所提出的VEF模型可解释为输运修正的扩散降阶模型。在模拟超声速辐射波前的Fleck-Cummings基准问题上展示了数值结果。与所考虑的辐射-扩散模型解相比，该VEF模型能可靠地将TRT问题的计算精度提升1-2个数量级。