Solutions of Conformal Israel-Stewart Relativistic Viscous Fluid Dynamics

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.

11 pages, 16 figure. Tables with the semi-analytical solutions of Israel-Stewart theory are included in this submission

References in corpus (12)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Nonlinear Fluid Dynamics from Gravity
• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Elliptic and triangular flow in event-by-event (3+1)D viscous hydrodynamics
• Dissipative relativistic fluid dynamics: a new way to derive the equations of motion from kinetic theory
• Stability and Causality in relativistic dissipative hydrodynamics
• Origin of the Relaxation Time in Dissipative Fluid Dynamics
• Studies of azimuthal dihadron correlations in ultra-central PbPb collisions at sqrt(s[NN]) = 2.76 TeV
• Relativistic viscous hydrodynamics for heavy-ion collisions with ECHO-QGP
• A New Family of Simple Solutions of Perfect Fluid Hydrodynamics
• Exact analytical solutions of second-order conformal hydrodynamics
• A systematic study of exact solutions in second-order conformal hydrodynamics

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