📝 SummarXiv

Abstract

We present here a new hybrid scheme that combines a discontinuous Galerkin (DG) method with compact finite volume (FV) and finite difference (FD) methods. The computational mesh is divided into smaller elements that touch but do not overlap. Like a pure DG method, our new hybrid scheme requires information exchange only at the surface of neighboring elements. This avoids the need for ghost zones that are usually many points deep in traditional FV implementations. Furthermore, unlike traditional FV implementations, that need information exchange between each element and its 26 surrounding neighbors on noncuboid meshes, our new hybrid method exchanges information only between each element and its six nearest neighbors. With this reduced communication, we aim to retain the high scalability of DG when using large supercomputers. In addition, the information exchange between adjacent elements is much simpler than in a traditional FV implementation, because we always have grid points at the interface, so that only surface interpolation is required. As a result it is much easier to implement adaptive mesh refinement. The goal is to use DG in elements with smooth matter fields and to fall back onto the more robust FV/FD method in elements that contain nonsmooth shocks or star surfaces. For this we devise trouble criteria to decide whether an element should be evolved with DG or FV/FD. We use the Nmesh program to implement and test the new scheme. We successfully evolve various single neutron star cases. These include the challenging cases of a neutron star initially in an unstable equilibrium migrating to a stable configuration and a boosted neutron star. These cases are simulated for the first time here in full 3D with general relativistic hydrodynamics using DG methods. We also describe additional numerical methods, such as the limiters and the atmosphere treatment we need for our simulations.