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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$2 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
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  • TXT
@Article{IJNAM-17-118, author = {Li , Ruo and Li , Weiming}, 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$2 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$2 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.

Li , Ruo and Li , Weiming. (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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