Discontinuous Galerkin finite element methods for radiative transfer in spherical symmetry

¹ Physikalisches Institut & Center for Space and Habitability, University of Bern, Sidlerstr. 5, 3012 Bern, Switzerland
e-mail: daniel.kitzmann@csh.unibe.ch
² Zentrum für Astronomie und Astrophysik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany

Received: 23 March 2016
Accepted: 24 July 2016

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 owing 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.