Radiation-magnetohydrodynamics with MPI-AMRVAC using flux-limited diffusion

Context. Radiation plays a significant role in solar and astrophysical environments, as it may constitute a sizable fraction of the energy density, momentum flux, and total pressure. Modeling the dynamic interaction between radiation and magnetized plasmas in such environments is an intricate and computationally costly task. Aims. The goal of this work is to demonstrate the capabilities of the open-source parallel, block-adaptive computational framework MPI-AMRVAC in solving equations of radiation-magnetohydrodynamics (RMHD) and to present benchmark test cases relevant for radiation-dominated magnetized plasmas. Methods. We combined the existing magnetohydrodynamics (MHD) and flux-limited diffusion (FLD) radiative-hydrodynamics physics modules to solve the equations of RMHD on block-adaptive finite volume Cartesian meshes in any dimensionality. Results. We introduce and validate several benchmark test cases, such as steady radiative MHD shocks, radiation-damped linear MHD waves, radiation-modified Riemann problems, and a multi-dimensional radiative magnetoconvection case. We recall the basic governing Rankine-Hugoniot relations for shocks and the dispersion relation for linear MHD waves in the presence of optically thick radiation fields where the diffusion limit is reached. The RMHD system allows for eight linear wave types, where the classical seven-wave MHD picture (entropy and three wave pairs for slow, Alfvén and fast) is augmented with a radiative diffusion mode. Conclusions. The MPI-AMRVAC code now has the capability to perform multidimensional RMHD simulations with mesh adaptation, making it well suited for larger scientific applications studying magnetized matter-radiation interactions in solar and stellar interiors and atmospheres.