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Explicit-implicit difference scheme for the joint solution of the radiative transfer and energy equations by the splitting method. (Russian, English) Zbl 1274.76269

Zh. Vychisl. Mat. Mat. Fiz. 53, No. 3, 442-458 (2013); translation in Comput. Math. Math. Phys. 53, No. 3, 320-335 (2013).
Summary: High-order accurate explicit and implicit conservative predictor-corrector schemes are presented for the radiative transfer and energy equations in the multigroup kinetic approximation solved together by applying the splitting method with respect to physical processes and spatial variables. The original system of integrodifferential equations is split into two subsystems: one of partial differential equations without sources and one of ordinary differential equations (ODE) with sources. The general solution of the ODE system and the energy equation is written in quadratures based on total energy conservation in a cell. A feature of the schemes is that a new approximation is used for the numerical fluxes through the cell interfaces. The fluxes are found along characteristics with the interaction between radiation and matter taken into account. For smooth solutions, the schemes approximating the transfer equations on spatially uniform grids are second-order accurate in time and space. As an example, numerical results for Fleck’s test problems are presented that confirm the increased accuracy and efficiency of the method.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
65N06 Finite difference methods for boundary value problems involving PDEs
45K05 Integro-partial differential equations

Software:

pchip; UNCMND
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References:

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