Simulating elliptic flow with viscous hydrodynamics

Abstract

In this work we simulate a viscous hydrodynamical model of noncentral Au-Au collisions in 2+1 dimensions, assuming longitudinal boost invariance. The model fluid equations were proposed by \"Ottinger and Grmela [Grmela, M., and \"Ottinger, H. C., Phys. Rev. E, 56, 6620 (1997)]. Freeze-out is signaled when the viscous corrections become large relative to the ideal terms. Then viscous corrections to the transverse momentum and differential elliptic flow spectra are calculated. When viscous corrections to the thermal distribution function are not included, the effects of viscosity on elliptic flow are modest. However, when these corrections are included, the elliptic flow is strongly modified at large ${p}_{T}$. We also investigate the stability of the viscous results by comparing the nonideal components of the stress tensor (${\ensuremath{\pi}}^{\mathit{ij}}$) and their influence on the ${v}_{2}$ spectrum to the expectation of the Navier-Stokes equations (${\ensuremath{\pi}}^{\mathit{ij}}=\ensuremath{-}\ensuremath{\eta}\ensuremath{\langle}\ensuremath{\partial}{}_{i}{u}_{j}\ensuremath{\rangle}$). We argue that when the stress tensor deviates from the Navier-Stokes form the dissipative corrections to spectra are too large for a hydrodynamic description to be reliable. For typical Relativistic Heavy Ion Colloder initial conditions this happens for $\ensuremath{\eta}/s\ensuremath{\gtrsim}0.3$.