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Volume 15, Issue 1-2
An Asymptotic Preserving Implicit Unified Gas Kinetic Scheme for Frequency-Dependent Radiative Transfer Equations

Wenjun Sun, Song Jiang & Kun Xu

Int. J. Numer. Anal. Mod., 15 (2018), pp. 134-153.

Published online: 2018-01

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  • 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.

  • Keywords

radiative transfer, frequency-dependent, asymptotic preserving, implicit unified gas kinetic scheme (IUGKS).

  • AMS Subject Headings

85A25, 85-08, 65M99

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

sun_wenjun@iapcm.ac.cn (Wenjun Sun)

jiang@iapcm.ac.cn (Song Jiang)

makxu@ust.hk (Kun Xu)

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  • TXT
@Article{IJNAM-15-134, author = {Sun , WenjunJiang , Song and Xu , Kun}, title = {An Asymptotic Preserving Implicit Unified Gas Kinetic Scheme for Frequency-Dependent Radiative Transfer Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {15}, number = {1-2}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/10560.html} }
TY - JOUR T1 - An Asymptotic Preserving Implicit Unified Gas Kinetic Scheme for Frequency-Dependent Radiative Transfer Equations AU - Sun , Wenjun AU - Jiang , Song AU - Xu , Kun JO - International Journal of Numerical Analysis and Modeling VL - 1-2 SP - 134 EP - 153 PY - 2018 DA - 2018/01 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/10560.html KW - radiative transfer, frequency-dependent, asymptotic preserving, implicit unified gas kinetic scheme (IUGKS). AB -

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.

Wenjun Sun, Song Jiang & Kun Xu. (2020). An Asymptotic Preserving Implicit Unified Gas Kinetic Scheme for Frequency-Dependent Radiative Transfer Equations. International Journal of Numerical Analysis and Modeling. 15 (1-2). 134-153. doi:
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