A Second Order Radiative Transfer Equation and Its Solution by Meshless Method with Application to Strongly Inhomogeneous Media

TL;DR

This paper introduces a second order radiative transfer equation (MSORTE) that overcomes singularity issues in inhomogeneous media, and develops a meshless collocation method to solve it with improved stability and accuracy.

Contribution

The paper proposes MSORTE, a novel second order radiative transfer equation, and develops a meshless solution method demonstrating superior stability and accuracy in complex media.

Findings

MSORTE overcomes singularity issues in inhomogeneous media.

The meshless method provides stable and accurate solutions.

The approach handles media with voids and discontinuous properties.

Abstract

A new second order form of radiative transfer equation (named MSORTE) is proposed, which overcomes the singularity problem of a previously proposed second order radiative transfer equation [J. Comput. Phys. 214 (2006) 12-40 (where it was termed SAAI), Numer. Heat Transfer B 51 (2007) 391-409] in dealing with inhomogeneous media where some locations have very small/zero extinction coefficient. The MSORTE contains a naturally introduced diffusion (or second order) term which provides better numerical property than the classic first order radiative transfer equation (RTE). The stability and convergence characteristics of the MSORTE discretized by central difference scheme is analyzed theoretically, and the better numerical stability of the second order form radiative transfer equations than the RTE when discretized by the central difference type method is proved. A collocation meshless method is developed based on the MSORTE to solve radiative transfer in inhomogeneous media. Several critical test cases are taken to verify the performance of the presented method. The collocation meshless method based on the MSORTE is demonstrated to be capable of stably and accurately solve radiative transfer in strongly inhomogeneous media, media with void region and even with discontinuous extinction coefficient.