Computational methods for thermal radiative transfer problems exhibit high computational costs and a prohibitive memory footprint when the spatial and directional domains are finely resolved. A strategy to reduce such computational costs is dynamical low-rank approximation (DLRA), which represents and evolves the solution on a low-rank manifold, thereby significantly decreasing computational and memory requirements. Efficient discretizations for the DLRA evolution equations need to be carefully constructed to guarantee stability while enabling mass conservation. In this work, we focus on the Su-Olson closure and derive a stable discretization through an implicit coupling of energy and radiation density. Moreover, we propose a rank-adaptive strategy to preserve local mass conservation. Numerical results are presented which showcase the accuracy and efficiency of the proposed method.

翻译：热辐射传输问题的计算方法在空间与方向维度精细分辨时，会面临高昂的计算成本与极大的内存占用。降低此类计算成本的一种策略是采用动态低秩逼近（DLRA），该方法将解表示并演化于低秩流形上，从而显著减少计算与内存需求。DLRA演化方程的高效离散格式需精心构建，以便在保证稳定性的同时实现质量守恒。本研究聚焦于Su-Olson闭合模型，通过能量与辐射密度的隐式耦合推导出稳定的离散格式。此外，我们提出一种秩自适应策略以保持局部质量守恒。数值实验结果展示了所提方法的准确性与高效性。