Simulating elliptic flow with viscous hydrodynamics

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In this work we simulate a viscous hydrodynamical model of non-central Au-Au collisions in 2+1 dimensions, assuming longitudinal boost invariance. The model fluid equations were proposed by Öttinger and Grmela OG. Freezeout 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 pₜ. We also investigate the stability of the viscous results by comparing the non-ideal components of the stress tensor (πij) and their influence on the v₂ spectrum to the expectation of the Navier-Stokes equations (πij = -η ∂ᵢ uⱼ). 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 RHIC initial conditions this happens for η/s 0.3.