Volume 17, Issue 1
3D B2 Model for Radiative Transfer Equation

Ruo Li & Weiming Li

DOI:

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

Published online: 2020-02

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  • Abstract

We proposed a 3D B2 model for the radiative transfer equation. The model is an extension of the 1D B2 model for the slab geometry. The 1D B2 model is an approximation to the 2nd order maximum entropy (M2) 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 M2closure by B2 ansatz. Same as the M2 closure, the ansatz of the new 3D B2 model has the capacity to capture both isotropic solutions and strongly peaked solutions. And beyond the M2 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
  • TXT
@Article{IJNAM-17-118, author = {Li , Ruo and Li , Weiming }, title = {3D B2 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 B2 model for the radiative transfer equation. The model is an extension of the 1D B2 model for the slab geometry. The 1D B2 model is an approximation to the 2nd order maximum entropy (M2) 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 M2closure by B2 ansatz. Same as the M2 closure, the ansatz of the new 3D B2 model has the capacity to capture both isotropic solutions and strongly peaked solutions. And beyond the M2 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 B2 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://dor.org/ UR - https://global-sci.org/intro/ijnam/13644.html KW - Radiative transfer, moment model, maximum entropy closure. AB -

We proposed a 3D B2 model for the radiative transfer equation. The model is an extension of the 1D B2 model for the slab geometry. The 1D B2 model is an approximation to the 2nd order maximum entropy (M2) 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 M2closure by B2 ansatz. Same as the M2 closure, the ansatz of the new 3D B2 model has the capacity to capture both isotropic solutions and strongly peaked solutions. And beyond the M2 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 B2 Model for Radiative Transfer Equation . International Journal of Numerical Analysis and Modeling. 17 (1). 118-150. doi:
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