An improved formulation of the relativistic hydrodynamics equations in 2D Cartesian coordinates

TL;DR

This paper introduces a new flux-conservative formulation of relativistic hydrodynamics equations in cylindrical coordinates, significantly reducing numerical errors and enabling more accurate simulations of astrophysical phenomena with cylindrical symmetry.

Contribution

The paper presents a novel formulation that rearranges key terms in relativistic hydrodynamics equations to minimize numerical errors in cylindrical coordinates.

Findings

Global truncation error reduced by one or more orders of magnitude.

Improved accuracy demonstrated in simulations of oscillating stars.

Enhanced resolution in shock-tube tests.

Abstract

A number of astrophysical scenarios possess and preserve an overall cylindrical symmetry also when undergoing a catastrophic and nonlinear evolution. Exploiting such a symmetry, these processes can be studied through numerical-relativity simulations at smaller computational costs and at considerably larger spatial resolutions. We here present a new flux-conservative formulation of the relativistic hydrodynamics equations in cylindrical coordinates. By rearranging those terms in the equations which are the sources of the largest numerical errors, the new formulation yields a global truncation error which is one or more orders of magnitude smaller than those of alternative and commonly used formulations. We illustrate this through a series of numerical tests involving the evolution of oscillating spherical and rotating stars, as well as shock-tube tests.