A Consistent, Moment-Based, Multiscale Solution Approach for Thermal Radiative Transfer Problems

We present an efficient numerical algorithm for solving the time-dependent grey thermal radiative transfer (TRT) equations. The algorithm utilizes the first two angular moments of the TRT equations (Quasi-diffusion (QD)) together with the material temperature equation to form a nonlinear low-order (LO) system. The LO system is solved via the Jacobian-free Newton-Krylov method. The combined high-order (HO) TRT and LO-QD system is used to bridge the diffusion and transport scales. In addition, a “consistency” term is introduced to make the truncation error in the LO system identical to the truncation error in the HO equation. The derivation of the consistency term is rather general; therefore, it can be extended to a variety of spatial and temporal discretizations.