Multigroup Radiation Magnetohydrodynamics Based on Discrete Ordinates including Compton Scattering

Abstract

Abstract We present a formulation and numerical algorithm to extend the scheme for gray radiation magnetohydrodynamics (MHD) developed by Jiang to include the frequency dependence via the multigroup approach. The entire frequency space can be divided into an arbitrary number of groups in the lab frame, and we follow the time-dependent evolution of frequency-integrated specific intensities along discrete rays inside each group. Spatial transport of photons is done in the lab frame while all the coupling terms are solved in the fluid rest frame. Lorentz transformation is used to connect different frames. The radiation transport equation is solved fully implicitly in time while the MHD equations are evolved explicitly so that time step is not limited by the speed of light. A finite volume approach is used for transport in both spatial and frequency spaces to conserve the radiation energy density and momentum. The algorithm includes photon absorption, electron scattering, as well as Compton scattering, which is calculated by solving the Kompaneets equation. The algorithm is accurate for a wide range of optical depth conditions and can handle both radiation-pressure- and gas-pressure-dominated flows. It works for both Cartesian and curvilinear coordinate systems with adaptive mesh refinement. We provide a variety of test problems including a radiating sphere, shadow test, absorption of a moving gas, Bondi-type flows, as well as a collection of test problems for thermal and bulk Compton scattering. We also discuss examples where frequency dependence can make a big difference compared with the gray approach.