Abstract: Title: "Viscous hydrodynamics for relativistic heavy-ion collisions"\ Speaker: Huichao Song, The Ohio State University

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 continue to work in regions where ideal hydrodynamics begins to fail. Using the 2nd order Israel-Stewart formulation of (2+1)-dimensional viscous hydrodynamics, we numerically study the effects from shear viscosity on particle spectra and elliptic flow $v_2$. We find that $v_2$ is very sensitive to the QGP shear viscosity. We compare results on the viscous suppression of elliptic flow from two different groups (Romatschke & Romatschke 2007 for Au+Au collisions, and Song & Heinz 2007-08 for Cu+Cu collisions) who have employed different variants of the Israel-Stewart equations. We assess the effects on viscous hydrodynamic evolution and hadron spectra of system size, equation of state, and the kinetic relaxation time when using different kinetic evolution equations for the viscous pressure tensor. We show that in the limit of zero relaxation time the different approaches agree numerically. Finally, we investigate the scaling of the eccentricity-scaled elliptic flow, $v_2/\\epsilon_x$, with the charged hadron multiplicity per overlap area, for Cu+Cu and Au+Au collisions at a variety of impact parameters and collision energies, for both ideal and viscous hydrodynamics.