3D $B$2 Model for Radiative Transfer Equation

Authors

  • Ruo Li HEDPS & CAPT, LMAM & School of Mathematical Sciences, Peking University, Beijing, China
  • Weiming Li Applied and Computational Mathematics Division, Beijing Computational Science Research Center, Beijing 100193, China and Department of Mathematics, The Hong Kong University of Science & Technology, Clear Water Bay, Kowloon, Hong Kong

Keywords:

Radiative transfer, moment model, maximum entropy closure.

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.

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Published

2021-02-04

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Issue

Vol. 17 No. 1 (2020)

Section

Articles