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.

中文翻译：

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内存减少的隐式方法用于热辐射传递

本文介绍了高能量密度物理学中与时间有关的热辐射传递问题的近似方法。它基于由高阶辐射传递方程（RTE）和低阶拟扩散（aka VEF）方程定义的多级拟扩散方法，用于特定强度的弯矩。时间步长之间的TRT问题中的大部分数据存储取决于辐射强度的网格函数的维数。对于时间相关的Boltzmann方程，使用减少了存储量的近似隐式方法应用于高阶RTE，并通过反向Euler（BE）方案及时离散化。BE方案中来自先前时间级别的高维强度是通过低秩适当正交分解（POD）进行近似的。所提出方法的另一种形式将POD应用于强度的P2扩展的剩余项。近似隐式方法的解的精度取决于POD的等级。所提出的方法使得能够减少与时间有关的问题中的存储需求。提出了Fleck-Cummings TRT测试问题的数值结果。