AN ALGORITHM FOR RADIATION MAGNETOHYDRODYNAMICS BASED ON SOLVING THE TIME-DEPENDENT TRANSFER EQUATION

Abstract

(Abridged) We describe a new algorithm for solving the coupled\nfrequency-integrated transfer equation and the equations of\nmagnetohydrodynamics when the light-crossing time is only marginally shorter\nthan dynamical timescales. The transfer equation is solved in the mixed frame,\nincluding velocity dependent source terms accurate to O(v/c). An operator split\napproach is used to compute the specific intensity along discrete rays, with\nupwind monotonic interpolation used along each ray to update the transport\nterms, and implicit methods used to compute the scattering and absorption\nsource terms. Conservative differencing is used for the transport terms, which\nensures the specific intensity (as well as energy and momentum) are conserved\nalong each ray to round-off error. The use of implicit methods for the source\nterms ensures the method is stable even if the source terms are very stiff. To\ncouple the solution of the transfer equation to the MHD algorithms in the\nAthena code, we perform direct quadrature of the specific intensity over angles\nto compute the energy and momentum source terms. We present the results of a\nvariety of tests of the method, such as calculating the structure of a non-LTE\natmosphere, an advective diffusion test, linear wave convergence tests, and the\nwell-known shadow test. We use new semi-analytic solutions for radiation\nmodified shocks to demonstrate the ability of our algorithm to capture the\neffects of an anisotropic radiation field accurately. Since the method uses\nexplicit differencing of the spatial operators, it shows excellent weak scaling\non parallel computers. The method is ideally suited for problems in which\ncharacteristic velocities are non-relativistic, but still within a few percent\nor more of the speed of light. The method is an intermediate step towards\nalgorithms for fully relativistic flows.\n