We review several facets of the hydrodynamic description of the relativistic heavy ion collisions, starting from the historical motivation to the present understandings of the observed collective aspects of experimental data, especially those of the
most recent RHIC and LHC results. In this report, we particularly focus on the conceptual questions and the physical foundations of the validity of the hydrodynamic approach itself. We also discuss recent efforts to clarify some of the points in this direction, such as the various forms of derivations of relativistic hydrodynamics together with the limitations intrinsic to the traditional approaches, variational approaches, known analytic solutions for special cases, and several new theoretical developments. Throughout this review, we stress the role of course-graining procedure in the hydrodynamic description and discuss its relation to the physical observables through the analysis of a hydrodynamic mapping of a microscopic transport model. Several questions to be answered to clarify the physics of collective phenomena in the relativistic heavy ion collisions are pointed out.
The transverse momentum anisotropy of the particles produced in heavy ion collisions is one of the most important experimental observable to investigate the collective behavior of the systems created in such collisions. Recent studies show that the c
omplex nature of the system evolution, such as initial condition fluctuations and jets, may lead to important effects in the flow coefficients and, therefore, to misinterpretation of the results obtained. In this study, we used simulated events produced with a hydrodynamic model which allows inhomogeneous initial condition combined with proton-proton collisions produced with the Pythia event generator to create a final set of particles to be analyzed with the usual experimental flow calculation techniques. Although this simplified approach is somehow unrealistic, since it does not include the interaction of the jet with the medium, our results have shown a good agreement of the behavior of the elliptic flow coefficient as a function of the transverse momentum up to 6 GeV/c for Au+Au collisions at 200 GeV. Although each model alone is not able to describe the full range, the combination of both sets of particles as seen by the flow calculation techniques may be the key to explain the behavior observed in experimental data.
We present a systematic study of the effects due to initial condition fluctuations in systems formed by heavy-ion collisions using the hydrodynamical simulation code NeXSPheRIO. The study was based on a sample of events generated simulating Au+Au col
lisions at center of mass energy of 200 GeV per nucleon pair with impact parameter ranging from most central to peripheral collisions. The capability of the NeXSPheRIO code to control and save the initial condition (IC) as well as the final state particles after the 3D hydrodynamical evolution allows for the investigation of the sensitivity of the experimental observables to the characteristics of the early IC. Comparisons of results from simulated events generated using fluctuating initial conditions and smooth initial condition are presented for the experimental observable elliptic flow parameter ($v_2$) as a function of the transverse momentum, $p_t$, and centrality. We compare $v_2$ values estimated using different methods, and how each method responds to effects of fluctuations in the initial condition. Finally, we quantify the flow fluctuations and compare to the fluctuations of the initial eccentricity of the energy density distribution in the transverse plane.
