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

TL;DR

This paper compares viscous fluid dynamics and kinetic theory in solving the relativistic Riemann problem, clarifying the validity regimes of second-order fluid models in relativistic shock phenomena.

Contribution

It provides a detailed comparison between Israel-Stewart fluid dynamics and kinetic theory, establishing validity conditions for modeling relativistic shocks.

Findings

Good agreement requires Knudsen number Kn < 1/2.

Transition from ideal to viscous shocks demonstrated by varying η/s.

Comparison clarifies the regime of validity for second-order fluid dynamics.

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 $Kn < 1/2$.