Hydrodynamics and Flow

The main purpose of the lecture was to lead students and young post-docs to the frontier of the hydrodynamic description of relativistic heavy-ion collisions (H.I.C.) in order for them to understand talks and posters presented in the Quark Matter 2008 (QM08) conference in Jaipur, India [1]. So the most recent studies were not addressed in this lecture as they would be presented during the QM08 conference itself. Also, we try to give a very pedagogical lecture here. For the readers who may want to study relativistic hydrodynamics and its application to H.I.C. as an advanced course, we strongly recommend them to consult the references. This lecture note is divided into three parts. In the first part we give a brief introduction to relativistic hydrodynamics in the context of H.I.C. In the second part we present the formalism and some fundamental aspects of relativistic ideal and viscous hydrodynamics. In the third part, we start with some basic checks of the fundamental observables followed by discussion of collective flow, in particular elliptic flow, which is one of the most exciting phenomenon in H.I.C. at relativistic energies. Next we discuss how to formulate the hydrodynamic model to describe dynamics of H.I.C. Finally, we conclude the third part of the lecture note by showing some results from ideal hydrodynamics calculations and by comparing them with the experimental data. We use the natural units c = h̄ = kB = 1 and the Minkowski metric g = diag(1,−1,−1,−1) throughout the lecture note.