Year: 2020
Author: Ruo Li, Weiming Li
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2020-IJNAM-13644
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 1 : pp. 118–150
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 33
Keywords: Radiative transfer moment model maximum entropy closure.