An Asymptotic Preserving Implicit Unified Gas Kinetic Scheme for Frequency-Dependent Radiative Transfer Equations
Year: 2018
Author: Wenjun Sun, Song Jiang, Kun Xu
International Journal of Numerical Analysis and Modeling, Vol. 15 (2018), Iss. 1-2 : pp. 134–153
Abstract
In this paper, an asymptotic preserving implicit unified gas kinetic scheme (IUGKS) is constructed for the frequency-dependent radiative transfer equations. Different from the asymptotic preserving unified gas kinetic scheme (UGKS) which uses the explicit initial value of the radiation intensity in the construction of the boundary fluxes as in the previous works [Sun et al., J. Comput. Phys. 285 (2015), pp. 265-279 and J. Comput. Phys. 302 (2015), pp. 222-238], here we construct the boundary fluxes by a back-time discretization so that they depend implicitly on the radiation intensity. Thus, the time step constraint by the Courant-Friedrichs-Lewy (CFL) condition is not needed anymore for IUGKS. It is shown that IUGKS is asymptotic preserving uniformly with the small Knudsen parameter. A number of numerical tests have been carried out and the numerical results show that large time steps can be used for the current scheme, and the computational efficiency can be improved greatly in comparison with UGKS and the implicit Monte Carlo scheme.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2018-IJNAM-10560
International Journal of Numerical Analysis and Modeling, Vol. 15 (2018), Iss. 1-2 : pp. 134–153
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: radiative transfer frequency-dependent asymptotic preserving implicit unified gas kinetic scheme (IUGKS).