Implicit Methods with Reduced Memory for Thermal Radiative Transfer
This work addresses the memory bottleneck in high-dimensional thermal radiative transfer simulations for high energy density physics, offering a practical reduction in storage requirements.
The paper introduces approximation methods for time-dependent thermal radiative transfer that reduce memory storage by using low-rank proper orthogonal decomposition (POD) to approximate the high-dimensional intensity from previous time steps. Numerical results on a Fleck-Cummings test problem demonstrate the effectiveness of the approach.
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.