High energy collisions of heavy nuclei are performed to investigate the high temperature regime of the strong interactions, especially properties of the expected deconfinement phase transition and the resulting color-deconfined phase of matter. I will discuss the (surprisingly successful) use of causal relativistic viscous hydrodynamics to model the evolution of the medium created in such collisions. Specifically, I will review my work (in collaboration with Paul Romatschke) using such simulations to constrain the value of the shear viscosity of the hot, strongly-interacting system created in 200 GeV Au+Au collisions at the Relativistic Heavy Ion Collider in Brookhaven. Using the knowledge thus gained, I will then present a prediction for the elliptic flow in the higher-energy Pb+Pb collisions to be performed at the LHC.

IPhT