TY - JOUR
T1 - 3D $B$<sub>2</sub> 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 - <p style="text-align: justify;">We proposed a 3D $B$<sub>2</sub> model for the radiative transfer equation. The model is an
extension of the 1D $B$<sub>2</sub> model for the slab geometry. The 1D $B$<sub>2</sub> model is an approximation to the
2nd order maximum entropy ($M$<sub>2</sub>) 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 $M$<sub>2&nbsp;</sub>closure by $B$<sub>2</sub> ansatz. Same as the $M$<sub>2</sub> closure, the ansatz of the new 3D $B$<sub>2</sub> model has the capacity
to capture both isotropic solutions and strongly peaked solutions. And beyond the $M$<sub>2</sub> 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.</p>