Solutions of Conformal Israel-Stewart Relativistic Viscous Fluid Dynamics

TL;DR

This paper constructs explicit analytical and semi-analytical solutions for the Israel-Stewart relativistic viscous hydrodynamics equations with radial expansion, aiding the validation of numerical simulations of quark-gluon plasma.

Contribution

It provides the first explicit solutions for radially-expanding Israel-Stewart hydrodynamics using symmetry arguments, including an exact solution in the cold plasma limit.

Findings

Analytical solutions match numerical simulations from MUSIC code.

Solutions serve as benchmarks for viscous hydrodynamics algorithms.

Explicit solutions help validate modeling of quark-gluon plasma.

Abstract

We use symmetry arguments developed by Gubser to construct the first radially-expanding explicit solutions of the Israel-Stewart formulation of hydrodynamics. Along with a general semi-analytical solution, an exact analytical solution is given which is valid in the cold plasma limit where viscous effects from shear viscosity and the relaxation time coefficient are important. The radially expanding solutions presented in this paper can be used as nontrivial checks of numerical algorithms employed in hydrodynamic simulations of the quark-gluon plasma formed in ultra-relativistic heavy ion collisions. We show this explicitly by comparing such analytic and semi-analytic solutions with the corresponding numerical solutions obtained using the MUSIC viscous hydrodynamics simulation code.