A Nonlinear Moment Model for Radiative Transfer Equation

TL;DR

This paper introduces a nonlinear moment model for the 3D radiative transfer equation that offers mathematical robustness and accuracy, validated through numerical simulations.

Contribution

It extends the nonlinear moment model from slab geometry to 3D space, achieving global hyperbolicity and spectral accuracy.

Findings

Model exhibits global hyperbolicity and rotational invariance

Achieves spectral accuracy and correct higher-order Eddington approximation

Numerical simulations validate the model's effectiveness

Abstract

We derive a nonlinear moment model for radiative transfer equation in 3D space, using the method to derive the nonlinear moment model for the radiative transfer equation in slab geometry. The resulted 3D HMPN model enjoys a list of mathematical advantages, including global hyperbolicity, rotational invariance, physical wave speeds, spectral accuracy, and correct higher-order Eddington approximation. Simulation examples are presented to validate the new model numerically.