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/2020-IJNAM-13644}, url = {https://global-sci.com/article/83012/3d-bsub2sub-model-for-radiative-transfer-equation} }