3D B_2 Model for Radiative Transfer Equation Part I: Modelling
This work provides a computationally tractable and hyperbolic closure for radiative transfer in 3D, benefiting researchers in computational physics and engineering who need efficient simulations of radiative transport.
The authors extend the approximate M_2 model for radiative transfer from slab geometry to three dimensions, creating a globally hyperbolic B_2 model with closed-form fluxes that captures both isotropic and beam-like solutions, enabling practical numerical simulations.
We extend to three-dimensional space the approximate M_2 model for the slab geometry studied in our previous paper. The B_2 model therein, as a special case of the second order extended quadrature method of moments (EQMOM), is proved to be globally hyperbolic. The model we proposed here extends EQMOM to multiple dimensions following the idea to approximate the maximum entropy closure for the slab geometry case. Like the M_2 closure, the ansatz of the new model has the capacity to capture both isotropic and beam-like solutions, while the new model has fluxes in closed-form, thus is applicable to practical numerical simulations. The rotational invariance, realizability, and hyperbolicity of the model are studied.