A high order special relativistic hydrodynamic and magnetohydrodynamic code with spacetime adaptive mesh refinement
We present a high order one-step ADERWENO finite volume scheme with spacetime 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 RungeKutta sub-steps. This turns out to be particularly advantageous in combination with spacetime 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. We also compare two different Riemann solvers for the computation of the numerical fluxes at the cell interfaces. The new scheme has been validated over a sample of numerical test problems in one, two and three spatial dimensions, exploring its ability in resolving the propagation of relativistic hydrodynamical and magnetohydrodynamical waves in different physical regimes. The astrophysical relevance of the new code for the study of the RichtmyerMeshkov instability is briefly discussed in view of future applications.
magnetohydrodynamics spacetime adaptive mesh refinement (amr) time-accurate local time stepping (lts) special relativity high order aderweno finite volume scheme