Hydrodynamics in full general relativity with conservative AMR

TL;DR

This paper introduces a numerical relativity code that combines hydrodynamics with Einstein's equations, utilizing adaptive mesh refinement and flux correction techniques to accurately simulate matter in strong gravitational fields, relevant for neutron star mergers.

Contribution

The paper presents a new computational framework integrating conservative hydrodynamics with general relativity using AMR and flux corrections, tailored for binary neutron star merger simulations.

Findings

Code successfully simulates eccentric black hole-neutron star mergers.

Implementation of flux correction algorithms improves conservation across AMR boundaries.

Performance tests demonstrate the effectiveness of different limiters and flux calculation methods.

Abstract

There is great interest in numerical relativity simulations involving matter due to the likelihood that binary compact objects involving neutron stars will be detected by gravitational wave observatories in the coming years, as well as to the possibility that binary compact object mergers could explain short-duration gamma-ray bursts. We present a code designed for simulations of hydrodynamics coupled to the Einstein field equations targeted toward such applications. This code has recently been used to study eccentric mergers of black hole-neutron star binaries. We evolve the fluid conservatively using high-resolution shock-capturing methods, while the field equations are solved in the generalized-harmonic formulation with finite differences. In order to resolve the various scales that may arise, we use adaptive mesh refinement (AMR) with grid hierarchies based on truncation error estimates. A noteworthy feature of this code is the implementation of the flux correction algorithm of Berger and Colella to ensure that the conservative nature of fluid advection is respected across AMR boundaries. We present various tests to compare the performance of different limiters and flux calculation methods, as well as to demonstrate the utility of AMR flux corrections.