High-order fully general-relativistic hydrodynamics: new approaches and tests

Abstract

We present a new approach for achieving high-order convergence in fully\ngeneral-relativistic hydrodynamic simulations. The approach is implemented in\nWhiskyTHC, a new code that makes use of state-of-the-art numerical schemes and\nwas key in achieving, for the first time, higher than second-order convergence\nin the calculation of the gravitational radiation from inspiraling binary\nneutron stars Radice et al. (2013). Here, we give a detailed description of the\nalgorithms employed and present results obtained for a series of classical\ntests involving isolated neutron stars. In addition, using the\ngravitational-wave emission from the late inspiral and merger of binary neutron\nstars, we make a detailed comparison between the results obtained with the new\ncode and those obtained when using standard second-order schemes commonly\nemployed for matter simulations in numerical relativity. We find that even at\nmoderate resolutions and for binaries with large compactness, the phase\naccuracy is improved by a factor 50 or more.\n