3D B_2 Model for Radiative Transfer Equation Part I: Modelling

TL;DR

This paper introduces a new three-dimensional B_2 radiative transfer model extending previous slab geometry models, with proven hyperbolicity and practical flux computations, suitable for numerical simulations.

Contribution

The paper develops a 3D B_2 model based on EQMOM, extending previous 2D models, with proven hyperbolicity and closed-form fluxes for practical use.

Findings

Model is globally hyperbolic

Fluxes are in closed-form

Model captures isotropic and beam-like solutions

Abstract

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.