High-resolution shock capturing scheme for ideal hydrodynamics in general relativity optimized for quasistationary solutions

Abstract

In this article, we present a numerical scheme for relativistic ideal hydrodynamics on arbitrary curved spacetimes in up to three spatial dimensions. The aim of this scheme is an improved treatment of stationary or quasistationary scenarios without loss of general applicability. This is achieved by treating pressure and gravitational forces, which are usually computed with unrelated numerical methods, within a unified framework. We derive a special formulation of the source terms in the hydrodynamic evolution equations, which is then utilized to construct the new scheme. For single star simulations, the optimizations take full effect only for rigidly rotating isentropic stars in a corotating coordinate frame. To test the algorithm, simulations of single polytropic neutron stars (rigidly rotating and nonrotating) have been carried out, demonstrating its usefulness for studies of stellar oscillation modes. We found that most of the numerical error is caused by the treatment of the stellar surface. To study the evolution scheme itself, we introduce a test bed involving an artificial spacetime without a fluid-vacuum boundary. The oscillation modes of the stellar models used here have already been investigated in the literature. A comparison with our results is given, exhibiting good agreement.