Investigation of shock waves in the relativistic Riemann problem: A comparison of viscous fluid dynamics to kinetic theory

Abstract

We solve the relativistic Riemann problem in viscous matter using the relativistic Boltzmann equation and the relativistic causal dissipative fluid-dynamical approach of Israel and Stewart. Comparisons between these two approaches clarify and point out the regime of validity of second-order fluid dynamics in relativistic shock phenomena. The transition from ideal to viscous shocks is demonstrated by varying the shear viscosity to entropy density ratio $\eta /s$. We also find that a good agreement between these two approaches requires a Knudsen number $Kn<1/2$.

Version as published in PRC 82, 024910 (2010); 16 pages, 16 figures, typos corrected

References in corpus (17)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• On the Strongly-Interacting Low-Viscosity Matter Created in Relativistic Nuclear Collisions
• Hydrodynamic Models for Heavy Ion Collisions
• Does stability of relativistic dissipative fluid dynamics imply causality?
• Perturbative QCD Calculations of Elliptic Flow and Shear Viscosity in Au+Au Collisions at $\sqrt{s_{NN}}=200$ GeV
• Third-order relativistic dissipative hydrodynamics
• Lattice Boltzmann scheme for relativistic fluids
• Shear Viscosity in a Gluon Gas
• The applicability of causal dissipative hydrodynamics to relativistic heavy ion collisions
• Transport rates and momentum isotropization of gluon matter in ultrarelativistic heavy-ion collisions
• Elliptic flow of gluon matter in ultrarelativistic heavy-ion collisions
• Numerical tests of causal relativistic dissipative fluid dynamics
• Shock propagation and stability in causal dissipative hydrodynamics
• Development of relativistic shock waves in viscous gluon matter
• Dependence of elliptic flow on number of parton degrees of freedom
• Comparing the first and second order theories of relativistic dissipative fluid dynamics using the 1+1 dimensional relativistic flux corrected transport algorithm
• Relativistic Shock Waves and Mach Cones in Viscous Gluon Matter

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