Solving 3D relativistic hydrodynamical problems with WENO discontinuous Galerkin methods

Discontinuous Galerkin (DG) methods coupled to WENO algorithms allow high order convergence for smooth problems and for the simulation of discontinuities and shocks. In this work, we investigate WENO-DG algorithms in the context of numerical general relativity, in particular for general relativistic hydrodynamics. We implement the standard WENO method at different orders, a compact (simple) WENO scheme, as well as an alternative subcell evolution algorithm. To evaluate the performance of the different numerical schemes, we study non-relativistic, special relativistic, and general relativistic testbeds. We present the first three-dimensional simulations of general relativistic hydrodynamics, albeit for a fixed spacetime background, within the framework of WENO-DG methods. The most important testbed is a single TOV-star in three dimensions, showing that long term stable simulations of single isolated neutron stars can be obtained with WENO-DG methods.