An Algorithm for Radiation Magnetohydrodynamics Based on Solving the Time-Dependent Transfer Equation

Abstract

We describe a new algorithm for solving the coupled frequency-integrated transfer equation and the equations of magnetohydrodynamics in the regime that light-crossing time is only marginally shorter than dynamical timescales. The transfer equation is solved in the mixed frame, including velocity-dependent source terms accurate to O(v/c). An operator split approach is used to compute the specific intensity along discrete rays, with upwind monotonic interpolation used along each ray to update the transport terms, and implicit methods used to compute the scattering and absorption source terms. Conservative differencing is used for the transport terms, which ensures the specific intensity (as well as energy and momentum) are conserved along each ray to round-off error. The use of implicit methods for the source terms ensures the method is stable even if the source terms are very stiff. To couple the solution of the transfer equation to the MHD algorithms in the Athena code, we perform direct quadrature of the specific intensity over angles to compute the energy and momentum source terms. We present the results of a variety of tests of the method, such as calculating the structure of a non-LTE atmosphere, an advective diffusion test, linear wave convergence tests, and the well-known shadow test. We use new semi-analytic solutions for radiation modified shocks to demonstrate the ability of our algorithm to capture the effects of an anisotropic radiation field accurately. Since the method uses explicit differencing of the spatial operators, it shows excellent weak scaling on parallel computers.

A Global Three-Dimensional Radiation Magneto-Hydrodynamic Simulation of Super-Eddington Accretion Disks

“…The ideal MHD equations coupled with the time-dependent radiative transfer equations we solve are (Jiang et al 2014a)…”

“…We solve the above radiation MHD equations with the recently developed radiative transfer algorithm in Athena as described in Jiang et al (2014a). Cylindrical coordinates (Skinner & Ostriker 2010) with axes (r, φ, z) are used here, but the angles of specific intensities are kept fixed as in the Cartesian case.…”

“…Because of the approximations made in FLD and M1, they cannot accurately capture the angular distribution of the photons near the photosphere (Y.-F. Jiang et al, in preparation). Since we have developed a more accurate numerical algorithm to solve the time-dependent radiative transfer equations directly Davis et al 2012;Jiang et al 2014a), we repeat these calculations without adopting previous approximations. Although the slim disk model correctly determines that advection along the radial direction is more rapid than radiative diffusion along the vertical direction, advection in the vertical direction is not considered, nor have global numerical simulations identified vertical advection as playing a significant role.…”

“…We solve the full radiative transfer equation in the Newtonian limit without adopting any FLDor M1-like approximations (Jiang et al 2014a). Due to the large computational expense of our calculations, we have only completed one simulation with enough resolution to reach inflow equilibrium for a small radial range.…”

hero – A 3D general relativistic radiative post-processor for accretion discs around black holes

“…The limitations of the various methods mentioned above led to the development of more deterministic discretized finite-differencing methods (Stenholm, Stoerzer, & Wehrse 1991;Steinacker, Bacmann, & Henning 2002) and discrete ordinates characteristic methods (Dullemond & Turolla 2000;Steinacker, Bacmann, & Henning 2002;Hayes & Norman 2003;Vögler et al 1982;Heinemann et al 2006;Woitke, Kamp & Thi 2009;Hayek et al 2010;Davis et al 2012;Jiang et al 2014), which have a number of widely discussed advantages. However, all of these methods suffer from the phenomenon of "ray-defects" (see appendix A for a detailed discussion).…”