An adaptive moving mesh discontinuous Galerkin method for the radiative transfer equation

TL;DR

This paper introduces an adaptive moving mesh discontinuous Galerkin method combined with the discrete ordinate method to efficiently solve the high-dimensional radiative transfer equation, capturing sharp layers and improving accuracy.

Contribution

It presents a novel adaptive moving mesh discontinuous Galerkin approach with dynamic mesh adaptation for the radiative transfer equation, enhancing computational efficiency and accuracy.

Findings

Demonstrates improved accuracy in 1D and 2D numerical examples.

Shows efficient handling of sharp layers and discontinuities.

Validates the effectiveness of mesh adaptation strategy.

Abstract

The radiative transfer equation models the interaction of radiation with scattering and absorbing media and has important applications in various fields in science and engineering. It is an integro-differential equation involving time, space and angular variables and contains an integral term in angular directions while being hyperbolic in space. The challenges for its numerical solution include the needs to handle with its high dimensionality, the presence of the integral term, and the development of discontinuities and sharp layers in its solution along spatial directions. Its numerical solution is studied in this paper using an adaptive moving mesh discontinuous Galerkin method for spatial discretization together with the discrete ordinate method for angular discretization. The former employs a dynamic mesh adaptation strategy based on moving mesh partial differential equations to improve computational accuracy and efficiency. Its mesh adaptation ability, accuracy, and efficiency are demonstrated in a selection of one- and two-dimensional numerical examples.