Causal Viscous Hydrodynamics in 2+1 Dimensions

The viscosity of the QGP is a hotly debated theoretical subject, and first principles calculations are difficult. It is thus important to try to extract the viscosity from experimental data. Viscous hydrodynamics provides a tool that can attack this problem and which may work in regions where ideal hydrodynamics fails. Using the 2nd order Israel-Stewart formulation of (2+1)- dimensional viscous hydrodynamics, we numerically study the effects from shear viscosity on the hydrodynamics evolution of a QGP, the final hadron spectra, and their elliptical flow coefficient $v_2$, for Cu+Cu collisions at RHIC. It turns out that the elliptic flow $v_2$ is very sensitive to the QGP shear viscosity, and that even the lowest bound, derived from AdS/CFT conjecture, $\eta/s=1/4\pi$, leads to a large suppression of $v_2$. We also explore the scaling behavior of $v_2$ with the initial source eccentricity $\varepsilon_x$, by computing $v_2/\varepsilon_x$ as a function of charged hadron multiplicity in both ideal hydrodynamics and viscous hydrodynamics, comparing Cu+Cu and Au+Au collisions at a variety of impact parameters and collision energies.