Numerical hydrodynamics in general relativity

TL;DR

This paper reviews the current state of numerical methods for solving ideal general relativistic hydrodynamics equations, emphasizing formulations, schemes, and astrophysical applications like black hole accretion and neutron star evolution.

Contribution

It provides an updated overview of numerical schemes, formulations, and astrophysical simulations in general relativistic hydrodynamics, highlighting recent advances and challenges.

Findings

Discussion of various numerical schemes and their effectiveness.

Summary of astrophysical simulations involving strong gravitational fields.

Analysis of numerical challenges in simulating black hole accretion and neutron stars.

Abstract

The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article the present update provides additional information on numerical schemes and extends the discussion of astrophysical simulations in general relativistic hydrodynamics. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A large sample of available numerical schemes is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of astrophysical simulations in strong gravitational fields is presented. These include gravitational collapse, accretion onto black holes and hydrodynamical evolutions of neutron stars. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances on the formulation of the gravitational field and hydrodynamic equations and the numerical methodology designed to solve them.