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An efficient and time accurate, moment-based scale-bridging algorithm for thermal radiative transfer problems. (English) Zbl 1285.65092
Physics-based preconditioning and a time-stepping strategy for a moment-based scale-bridging algorithm applied to the thermal radiative transfer equation are presented. The goal is to obtain consistent solutions (asymptotically) correct in second order with respect to the time, without nonlinear iterations between the high-order (HO) transport equation and the low-order (LO) continuum system within an iteration step. The modified equation analysis shows that this can be achieved via a simple predictor-corrector time stepping that requires only one inversion of the transport operator per time step. The authors find a degradation in the order of convergence in case of multifrequency problems. The proposed physics-based preconditioning utilizes a combination of the nonlinear elimination technique and the Fleck-Cummings linearization. As a result, the LO system can be solved efficiently via a multigrid preconditioned Jacobian-free Newton-Krylov method. For a set of numerical test problems (one-dimensional gray as well as multifrequency Marshak wave problems, two-dimensional Tophat problem), the physics-based preconditioner reduces the number of GMRES (generalized minimal residual) iterations by a factor of 3–4 in comparison to a standard preconditioner for advection-diffusion. Furthermore, the performance of the proposed physics-based preconditioner is insensitive to the time-step size.
(Text based on the abstract of the author)

MSC:
65R20 Numerical methods for integral equations
65H10 Numerical computation of solutions to systems of equations
85A25 Radiative transfer in astronomy and astrophysics
65F08 Preconditioners for iterative methods
65F10 Iterative numerical methods for linear systems
82C70 Transport processes in time-dependent statistical mechanics
82-08 Computational methods (statistical mechanics) (MSC2010)
45K05 Integro-partial differential equations
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