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This paper presents approximation methods for time-dependent thermalradiative transfer problems in high energy density physics. It is based on themultilevel quasidiffusion method defined by the high-order radiative transferequation (RTE) and the low-order quasidiffusion (aka VEF) equations for themoments of the specific intensity. A large part of data storage in TRT problemsbetween time steps is determined by the dimensionality of grid functions of theradiation intensity. The approximate implicit methods with reduced memory forthe time-dependent Boltzmann equation are applied to the high-order RTE,discretized in time with the backward Euler (BE) scheme. The high-dimensionalintensity from the previous time level in the BE scheme is approximated bymeans of the low-rank proper orthogonal decomposition (POD). Another version ofthe presented method applies the POD to the remainder term of P2 expansion ofthe intensity. The accuracy of the solution of the approximate implicit methodsdepends of the rank of the POD. The proposed methods enable one to reducestorage requirements in time dependent problems. Numerical results of aFleck-Cummings TRT test problem are presented.

Implicit Methods with Reduced Memory for Thermal Radiative Transfer