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Volume 17, Issue 1
3D $B$2 Model for Radiative Transfer Equation

Ruo Li & Weiming Li

Int. J. Numer. Anal. Mod., 17 (2020), pp. 118-150.

Published online: 2020-02

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  • Abstract

We proposed a 3D $B$2 model for the radiative transfer equation. The model is an extension of the 1D $B$2 model for the slab geometry. The 1D $B$2 model is an approximation to the 2nd order maximum entropy ($M$2) closure and has been proved to be globally hyperbolic. In 3D space, we are basically following the method for the slab geometry case to approximate the $M$closure by $B$2 ansatz. Same as the $M$2 closure, the ansatz of the new 3D $B$2 model has the capacity to capture both isotropic solutions and strongly peaked solutions. And beyond the $M$2 closure, the new model has fluxes in closed-form such that it is applicable to practical numerical simulations. The rotational invariance, realizability, and hyperbolicity of the new model are carefully studied.

  • Keywords

Radiative transfer, moment model, maximum entropy closure.

  • AMS Subject Headings

35Q35, 82C70

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

rli@math.pku.edu.cn (Ruo Li)

liweiming@csrc.ac.cn (Weiming Li)

  • BibTex
  • RIS
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@Article{IJNAM-17-118, author = {Ruo and Li and rli@math.pku.edu.cn and 11641 and HEDPS and CAPT, LMAM and School of Mathematical Sciences, Peking University, Beijing, China and Ruo Li and Weiming and Li and liweiming@csrc.ac.cn and 6540 and Applied and Computational Mathematics Division, Beijing Computational Science Research Center, Beijing 100193, China and Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong and Weiming Li}, title = {3D $B$2 Model for Radiative Transfer Equation }, journal = {International Journal of Numerical Analysis and Modeling}, year = {2020}, volume = {17}, number = {1}, pages = {118--150}, abstract = {

We proposed a 3D $B$2 model for the radiative transfer equation. The model is an extension of the 1D $B$2 model for the slab geometry. The 1D $B$2 model is an approximation to the 2nd order maximum entropy ($M$2) closure and has been proved to be globally hyperbolic. In 3D space, we are basically following the method for the slab geometry case to approximate the $M$closure by $B$2 ansatz. Same as the $M$2 closure, the ansatz of the new 3D $B$2 model has the capacity to capture both isotropic solutions and strongly peaked solutions. And beyond the $M$2 closure, the new model has fluxes in closed-form such that it is applicable to practical numerical simulations. The rotational invariance, realizability, and hyperbolicity of the new model are carefully studied.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/13644.html} }
TY - JOUR T1 - 3D $B$2 Model for Radiative Transfer Equation AU - Li , Ruo AU - Li , Weiming JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 118 EP - 150 PY - 2020 DA - 2020/02 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/13644.html KW - Radiative transfer, moment model, maximum entropy closure. AB -

We proposed a 3D $B$2 model for the radiative transfer equation. The model is an extension of the 1D $B$2 model for the slab geometry. The 1D $B$2 model is an approximation to the 2nd order maximum entropy ($M$2) closure and has been proved to be globally hyperbolic. In 3D space, we are basically following the method for the slab geometry case to approximate the $M$closure by $B$2 ansatz. Same as the $M$2 closure, the ansatz of the new 3D $B$2 model has the capacity to capture both isotropic solutions and strongly peaked solutions. And beyond the $M$2 closure, the new model has fluxes in closed-form such that it is applicable to practical numerical simulations. The rotational invariance, realizability, and hyperbolicity of the new model are carefully studied.

Ruo Li & Weiming Li. (2020). 3D $B$2 Model for Radiative Transfer Equation . International Journal of Numerical Analysis and Modeling. 17 (1). 118-150. doi:
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