A Nonlinear Moment Model for Radiative Transfer Equation in Slab Geometry

TL;DR

This paper introduces a novel nonlinear moment model for the radiative transfer equation in slab geometry, combining features of $P_N$ and $M_N$ models to better approximate anisotropic distributions with improved numerical efficiency.

Contribution

The paper develops a new moment model inspired by $P_N$ and $M_N$ models, incorporating the $M_1$ weight function to enhance anisotropic approximation capabilities.

Findings

The model is mathematically proven to be hyperbolic.

Numerical simulations show the model's superior accuracy and efficiency.

The model effectively captures anisotropic radiative transfer in slab geometry.

Abstract

This paper is concerned with the approximation of the radiative transfer equation for a grey medium in the slab geometry by the moment method. We develop a novel moment model inspired by the classical $P_N$ model and $M_N$ model. The new model takes the ansatz of the $M_1$ model as the weight function and follows the primary idea of the $P_N$ model to approximate the specific intensity by expanding it around the weight function in terms of orthogonal polynomials. The weight function uses the information of the first two moments, which brings the new model the capability to approximate an anisotropic distribution. Mathematical properties of the moment model are investigated, and particularly the hyperbolicity and the characteristic structure of the Riemann problem of the model with three moments are studied in detail. Some numerical simulations demonstrate its numerical efficiency and show its superior in comparison to the $P_N$ model.