A discrete-ordinate discontinuous-streamline diffusion method for the radiative transfer equation

TL;DR

This paper introduces a novel discrete-ordinate discontinuous-streamline diffusion method for the radiative transfer equation, combining discrete-ordinate and diffusion techniques to improve accuracy and stability in solutions.

Contribution

The paper develops a new DODSD method that incorporates artificial diffusion in the test functions, enhancing accuracy over existing DODG methods for the RTE.

Findings

The DODSD method provides more accurate solutions than the DODG method.

Stability and error estimates are rigorously established.

Numerical results confirm improved approximation quality.

Abstract

The radiative transfer equation (RTE) arises in many different areas of science and engineering. In this paper, we propose and investigate a discrete-ordinate discontinuous-streamline diffusion (DODSD) method for solving the RTE, which is a combination of the discrete-ordinate technique and the discontinuous-streamline diffusion method. Different from the discrete-ordinate discontinuous Galerkin (DODG) method for the RTE, an artificial diffusion parameter is added to the test functions in the spatial discretization. Stability and error estimates in certain norms are proved. Numerical results show that the proposed method can lead to a more accurate approximation in comparison with the DODG method.