Abstract

We describe numerical methods for solving the equations of radiation magnetohydrodynamics (MHD) for astrophysical fluid flow. Such methods are essential for the investigation of the time-dependent and multidimensional dynamics of a variety of astrophysical systems, although our particular interest is motivated by problems in star formation. Over the past few years, the authors have been members of two parallel code development efforts, and this review reflects that organization. In particular, we discuss numerical methods for MHD as implemented in the Athena code, and numerical methods for radiation hydrodynamics as implemented in the Orion code. We discuss the challenges introduced by the use of adaptive mesh refinement (AMR) in both codes, as well as the most promising directions for future developments.

Introduction

The dynamics of astrophysical systems described by the equations of radiation magnetohydrodynamics (MHD) span a tremendous range of scales and parameter regimes, from the interiors of stars (Kippenhahn & Weigert 1994), to accretion disks around compact objects (Turner et al. 2003), to dusty accretion flows around massive protostars (Krumholz et al. 2005, 2007a), to galactic-scale flows onto AGN (Thompson et al. 2005). All of these systems have in common that matter, radiation and magnetic fields are strongly interacting and that the energy and momentum carried by the radiation field is significant in comparison to that carried by the gas. Thus, an accurate treatment of the problem must include analysis of both the matter and the radiation, as well as the magnetic fields, and their mutual interaction.