Discontinuous Galerkin methods for general-relativistic hydrodynamics: formulation and application to spherically symmetric spacetimes

摘要

We have developed the formalism necessary to employ thediscontinuous-Galerkin approach in general-relativistic hydrodynamics. Theformalism is firstly presented in a general 4-dimensional setting and thenspecialized to the case of spherical symmetry within a 3+1 splitting ofspacetime. As a direct application, we have constructed a one-dimensional code,EDGES, which has been used to asses the viability of these methods via a seriesof tests involving highly relativistic flows in strong gravity. Our resultsshow that discontinuous Galerkin methods are able not only to handle strongrelativistic shock waves but, at the same time, to attain very high orders ofaccuracy and exponential convergence rates in smooth regions of the flow. Giventhese promising prospects and their affinity with a pseudospectral solution ofthe Einstein equations, discontinuous Galerkin methods could represent a newparadigm for the accurate numerical modelling in relativistic astrophysics.