Numerical viscosity in hydrodynamics simulations in general relativity

TL;DR

This paper introduces a new method to estimate numerical viscosity in astrophysical hydrodynamics simulations by analyzing fluid oscillation damping, aiding in understanding simulation accuracy and resolution needs.

Contribution

The paper presents an innovative approach to quantify numerical viscosity in relativistic hydrodynamics simulations, validated with controlled tests and applied to neutron star oscillations.

Findings

Numerical viscosity mainly originates from the star's surface.

The method effectively estimates viscosity in spherical and axisymmetric simulations.

Insights into resolution requirements for accurate astrophysical modeling.

Abstract

We present an alternative method to estimate the numerical viscosity in simulations of astrophysical objects, which is based in the damping of fluid oscillations. We apply the method to general relativistic hydrodynamic simulations using a spherical coordinates. We perform 1D-spherical and 2D- axisymmetric simulations of radial oscillations in spherical systems. We calibrate first the method with simulations with added bulk viscosity and study the differences between different numerical schemes. We apply the method to radial oscillations of neutron stars and we conclude that the main source of numerical viscosity in this case is the surface of the star. We expect that this method could be useful to compute the resolution requirements and limitations of the numerical simulations in different astrophysical scenarios in the future.