Excision methods for high resolution shock capturing schemes applied to general relativistic hydrodynamics

TL;DR

This paper introduces a straightforward excision boundary condition method for relativistic Euler equations within high-resolution shock capturing schemes, applicable without coordinate adaptation, and validated through various astrophysical tests.

Contribution

The paper presents a novel, simple excision boundary method compatible with standard HRSC schemes, tested on multiple relativistic hydrodynamics scenarios including black holes and neutron star collapse.

Findings

Effective excision boundary handling demonstrated in simulations

Compatibility with multiple reconstruction schemes shown

Modified PPM scheme resolves previous matching issues

Abstract

We present a simple method for applying excision boundary conditions for the relativistic Euler equations. This method depends on the use of Reconstruction-Evolution methods, a standard class of HRSC methods. We test three different reconstruction schemes, namely TVD, PPM and ENO. The method does not require that the coordinate system is adapted to the excision boundary. We demonstrate the effectiveness of our method using tests containing discontinuites, static test-fluid solutions with black holes, and full dynamical collapse of a neutron star to a black hole. A modified PPM scheme is introduced because of problems arisen when matching excision with the original PPM reconstruction scheme.