A GODUNOV METHOD FOR MULTIDIMENSIONAL RADIATION MAGNETOHYDRODYNAMICS BASED ON A VARIABLE EDDINGTON TENSOR

Abstract

We describe a numerical algorithm to integrate the equations of radiation\nmagnetohydrodynamics in multidimensions using Godunov methods. This algorithm\nsolves the radiation moment equations in the mixed frame, without invoking any\ndiffusion-like approximations. The moment equations are closed using a variable\nEddington tensor whose components are calculated from a formal solution of the\ntransfer equation at a large number of angles using the method of short\ncharacteristics. We use a comprehensive test suite to verify the algorithm,\nincluding convergence tests of radiation-modified linear acoustic and\nmagnetosonic waves, the structure of radiation modified shocks, and\ntwo-dimensional tests of photon bubble instability and the ablation of dense\nclouds by an intense radiation field. These tests cover a very wide range of\nregimes, including both optically thick and thin flows, and ratios of the\nradiation to gas pressure of at least 10^{-4} to 10^{4}. Across most of the\nparameter space, we find the method is accurate. However, the tests also reveal\nthere are regimes where the method needs improvement, for example when both the\nradiation pressure and absorption opacity are very large. We suggest\nmodifications to the algorithm that will improve accuracy in this case. We\ndiscuss the advantages of this method over those based on flux-limited\ndiffusion. In particular, we find the method is not only substantially more\naccurate, but often no more expensive than the diffusion approximation for our\nintended applications.\n