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 η/s. We also find that a good agreement between these two approaches requires a Knudsen number Kn < 1/2.

Investigation of Mach cones and the corresponding two-particle correlations in a microscopic transport model

“…These results are consistent with an investigation based on an AdS/CFT calculation [13] and a hydrodynamic model [14,15]. The comparison with the latter publications proofs once more BAMPS can model a hydrodynamic expansion [16,17]. Using the same non-expanding scenario, we studied the effect of dissipation in box scenario [12] and found that dissipation tends to destroy any Mach cone signal.…”

Thermalization in a small hadron gas system and high-multiplicity pp events

“…In hydrodynamical approach, the centrality dependent elliptic flow suggest [29,30] Kn ≈ 0.3 and 0.5 for the central and a semi-central AuAu events, respectively. A good agreement between the Boltzmann equation for dilute system and the relativistic dissipative fluid dynamics, the main tool to study the space-time evolution of the bulk matter formed in the relativistic heavy-ion collisions at RHIC, is established [31][32][33] for Kn< 0.5.…”

Hydrodynamic shock wave studies within a kinetic Monte Carlo approach

“…In the latter, particles can only interact with the walls of the simulation space but not with each other and λ can therefore be regarded as infinitely large. While mean free path studies have been performed for the Sod test [7,90], where results are compared to viscous hydrodynamic simulations, we are not aware of similar work that applied either the Noh or the Sedov problem. The setup and initialization of all tests is the same as in the continuum regime described in sections IV B, IV C, and IV D, whereas for the output we only analyze the spatial profiles of n, v, p, and T .…”

“…This is currently done in a Newtonian formalism but can be extended to a relativistic regime [6][7][8][9]72].…”

“…Simulations of shock structures [1] and hypersonic flow [2], studies of space flight [3] and nano-scale devices [4], particle production in heavy-ion collisions [5][6][7][8][9], the dynamics of inertial confinement fusion (ICF) capsules [10][11][12], and neutrino-matter interactions in core-collapse supernovae (CCSN) [13] are all examples of research areas which require the ability to model flows with K > 0.01. In our work we are especially interested in the modeling of ICF capsules and CCSN.…”