A Nonlinear Three-Moment Model for Radiative Transfer in Spherical Symmetry

TL;DR

This paper introduces a three-moment model using a beta distribution ansatz to effectively approximate radiative transfer in spherical symmetry, capturing anisotropy better than traditional methods.

Contribution

A novel three-moment model based on beta distribution ansatz for improved anisotropy representation in spherical radiative transfer.

Findings

Model accurately approximates radiative transfer in spherical symmetry.

Outperforms $P_n$ method in highly anisotropic cases.

Detailed analysis of the Riemann problem structure.

Abstract

We study the approximation of the radiative transfer equation with a relatively few moments in the spherically symmetric case. We propose a three-moment model based on choosing the beta distribution as the ansatz for the specific intensity. This ansatz enables our model to capture the anisotropy in the distribution function. The characteristic structure of the Riemann problem of the model is studied in detail. Numerical simulations demonstrate its validity in approximating the radiative transfer equation in the spherically symmetric case and its advantage in approximating highly anisotropic distribution functions in comparison to the $P_n$ method.