Robustness of a high-resolution central scheme for hydrodynamic simulations in full general relativity

TL;DR

This paper demonstrates that a high-resolution central scheme is effective and efficient for hydrodynamical simulations in full general relativity, accurately modeling neutron star oscillations and mergers without complex Riemann solvers.

Contribution

The study extends the application of a high-resolution central scheme to full general relativity, showing it matches traditional methods in accuracy while offering computational advantages.

Findings

HRC scheme yields accurate results comparable to HRSC schemes.

The scheme is computationally more efficient by avoiding Riemann problem solutions.

It effectively handles low-density atmospheres in neutron star simulations.

Abstract

A recent paper by Lucas-Serrano et al. indicates that a high-resolution central (HRC) scheme is robust enough to yield accurate hydrodynamical simulations of special relativistic flows in the presence of ultrarelativistic speeds and strong shock waves. In this paper we apply this scheme in full general relativity (involving {\it dynamical} spacetimes), and assess its suitability by performing test simulations for oscillations of rapidly rotating neutron stars and merger of binary neutron stars. It is demonstrated that this HRC scheme can yield results as accurate as those by the so-called high-resolution shock-capturing (HRSC) schemes based upon Riemann solvers. Furthermore, the adopted HRC scheme has increased computational efficiency as it avoids the costly solution of Riemann problems and has practical advantages in the modeling of neutron star spacetimes. Namely, it allows simulations with stiff equations of state by successfully dealing with very low-density unphysical atmospheres. These facts not only suggest that such a HRC scheme may be a desirable tool for hydrodynamical simulations in general relativity, but also open the possibility to perform accurate magnetohydrodynamical simulations in curved dynamic spacetimes.