Solving the system of radiation magnetohydrodynamics for solar physical simulations in 3d

In this study we present a finite-volumen scheme for solving the equations of radiation magnetohydrodynamics in two and three space dimensions. Among other applications this system is used to model the plasma in the solar convection zone and in the solar photosphere. It is a non--linear system of balance laws derived from the Euler equations of gas dynamics and the Maxwell equations; the energy transport through radiation is also included in the model. The starting point of our presentation is a standard explicit first and second order finite-volume scheme on both structured and unstructured grids. We first study the convergence of a finite-volume scheme applied to a scalar model problem for the full system of radiation magnetohydrodynamics. We then present modifications of the base scheme. These make it possible to approximate the system of magnetohydrodynamics with an arbitrary equation of state; they reduce errors due to a violation of the divergence constraint on the magnetic field, and they lead to an improved accuracy in the approximation of solution near an equilibrium state. These modifications significantly increase the robustness of the scheme and are essential for an accurate simulation of processes in the solar atmosphere ...thesi