This paper presents approximation methods for time-dependent thermal radiative transfer problems in high energy density physics. It is based on the multilevel quasidiffusion method defined by the high-order radiative transfer equation (RTE) and the low-order quasidiffusion (aka VEF) equations for the moments of the specific intensity. A large part of data storage in TRT problems between time steps is determined by the dimensionality of grid functions of the radiation intensity. The approximate implicit methods with reduced memory for the time-dependent Boltzmann equation are applied to the high-order RTE, discretized in time with the backward Euler (BE) scheme. The high-dimensional intensity from the previous time level in the BE scheme is approximated by means of the low-rank proper orthogonal decomposition (POD). Another version of the presented method applies the POD to the remainder term of P2 expansion of the intensity. The accuracy of the solution of the approximate implicit methods depends of the rank of the POD. The proposed methods enable one to reduce storage requirements in time dependent problems. Numerical results of a Fleck-Cummings TRT test problem are presented.

翻译：本文介绍了高能量密度物理学中基于时间的热辐射传导问题的近似方法,其依据是高阶辐射传导方程式(RTE)和特定强度时刻的低序准扩散方程式(aka VEF)界定的多级准扩散法(Aka VEF)和特定强度时段的低序准扩散方程式(POD)所定义的多级准扩散法(Aka VEF),在时间步骤之间的数据存储中的大部分问题是由辐射强度的网格功能的维度决定的,对时间依赖的Boltzmann方程式的内存减少的近似隐含方法适用于高序RTE,与落后的Euler(BE)方案同时分离。BE计划中前一个时间级的高维强度通过低级正或正向分解定位(POD)所近似。另一种方法将POD应用于强度扩展的P2剩余时期。近似隐含方法的解决方案的准确性取决于POD的等级。拟议方法可以减少时间依赖性的储存要求。