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We present a new numerical tool for solving the special relativistic idealMHD equations that is based on the combination of the following three keyfeatures: (i) a one-step ADER discontinuous Galerkin (DG) scheme that allowsfor an arbitrary order of accuracy in both space and time, (ii) an a posteriorisubcell finite volume limiter that is activated to avoid spurious oscillationsat discontinuities without destroying the natural subcell resolutioncapabilities of the DG finite element framework and finally (iii) a space-timeadaptive mesh refinement (AMR) framework with time-accurate localtime-stepping. The divergence-free character of the magnetic field is insteadtaken into account through the so-called "divergence-cleaning" approach. Theconvergence of the new scheme is verified up to 5th order in space and time andthe results for a set of significant numerical tests including shock tubeproblems, the RMHD rotor and blast wave problems, as well as the Orszag-Tangvortex system are shown. We also consider a simple case of the relativisticKelvin-Helmholtz instability with a magnetic field, emphasizing the potentialof the new method for studying turbulent RMHD flows. We discuss the advantagesof our new approach when the equations of relativistic MHD need to be solvedwith high accuracy within various astrophysical systems.

monthly notices of the royal astronomical society

Solving the relativistic magnetohydrodynamics equations with ADER  discontinuous Galerkin methods, a posteriori subcell limiting and adaptive  mesh refinement