A high order special relativistic hydrodynamic and magnetohydrodynamic code with space-time adaptive mesh refinement.

We present a high order one-step ADER–WENO finite volume scheme with space–time adaptive mesh refinement (AMR) for the solution of the special relativistic hydrodynamic and magnetohydrodynamic equations. By adopting a local discontinuous Galerkin predictor method, a high order one-step time discretization is obtained, with no need for Runge–Kutta sub-steps. This turns out to be particularly advantageous in combination with space–time adaptive mesh refinement, which has been implemented following a “cell-by-cell” approach. As in existing second order AMR methods, also the present higher order AMR algorithm features time-accurate local time stepping (LTS), where grids on different spatial refinement levels are allowed to use different time steps.