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

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(Abridged) We describe a new algorithm for solving the coupled frequency-integrated transfer equation and the equations of magnetohydrodynamics when the 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.