Multi-patch methods in general relativistic astrophysics - I. Hydrodynamical flows on fixed backgrounds

TL;DR

This paper introduces a numerical technique using multiple patches to effectively utilize spherical grids in fully relativistic astrophysical simulations, overcoming coordinate singularities.

Contribution

The paper presents a new multi-patch numerical scheme for simulating hydrodynamical flows on fixed backgrounds in relativistic astrophysics.

Findings

Successfully implemented multi-patch scheme for fixed background tests

Demonstrated effectiveness with accretion torus around a black hole

Provided detailed implementation instructions

Abstract

Many systems of interest in general relativistic astrophysics, including neutron stars, accreting compact objects in X-ray binaries and active galactic nuclei, core collapse, and collapsars, are assumed to be approximately spherically symmetric or axisymmetric. In Newtonian or fixed-background relativistic approximations it is common practice to use spherical polar coordinates for computational grids; however, these coordinates have singularities and are difficult to use in fully relativistic models. We present, in this series of papers, a numerical technique which is able to use effectively spherical grids by employing multiple patches. We provide detailed instructions on how to implement such a scheme, and present a number of code tests for the fixed background case, including an accretion torus around a black hole.