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A consistent, moment-based, multiscale solution approach for thermal radiative transfer problems. (English) Zbl 1278.82051
Summary: 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.

MSC:
82C70 Transport processes in time-dependent statistical mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)
82-08 Computational methods (statistical mechanics) (MSC2010)
65H10 Numerical computation of solutions to systems of equations
Software:
CASMO
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