Discontinuous Galerkin finite element methods for radiative transfer in spherical symmetry

TL;DR

This paper applies the discontinuous Galerkin finite element method to solve the radiative transfer equation in spherical symmetry, demonstrating its accuracy and ability to handle complex scattering and discontinuities in extended atmospheres.

Contribution

The paper develops a DG-FEM approach specifically for the spherically symmetric radiative transfer equation, enabling exact integration of complex scattering functions and improved handling of discontinuities.

Findings

Accurately models radiative transfer in spherical atmospheres

Handles complex scattering phase functions independently of angular resolution

Effectively captures discontinuities and complex behaviors in solutions

Abstract

The discontinuous Galerkin finite element method (DG-FEM) is successfully applied to treat a broad variety of transport problems numerically. In this work, we use the full capacity of the DG-FEM to solve the radiative transfer equation in spherical symmetry. We present a discontinuous Galerkin method to directly solve the spherically-symmetric radiative transfer equation as a two-dimensional problem. The transport equation in spherical atmospheres is more complicated than in the plane-parallel case due to the appearance of an additional derivative with respect to the polar angle. The DG-FEM formalism allows for the exact integration of arbitrarily complex scattering phase functions, independent of the angular mesh resolution. We show that the discontinuous Galerkin method is able to describe accurately the radiative transfer in extended atmospheres and to capture discontinuities or complex scattering behaviour which might be present in the solution of certain radiative transfer tasks and can, therefore, cause severe numerical problems for other radiative transfer solution methods.