Elliptic flow at RHIC is computed event by event with NeXSPheRIO. Reasonable agreement with experimental data on v2(eta) and v2(pt) is obtained. Various effects are studied as well: equation of state (with or without critical point), emission mechanism (Cooper-Frye prescription or continuous emission), type of the initial conditions (average or fluctuating initial conditions).

I present a brief overview on the motivation for performing relativistic nuclear collisions and the justification for using hydrodynamics to describe them. The contribution of Prof. Hama to the field of hydrodynamics and his efforts to form a group working on this subject are outlined.

A survey of various mechanisms for particle emission in hydrodynamics is presented. First, in the case of sudden freeze out, the problem of negative contributions in the Cooper-Frye formula and ways out are presented. Then the separate chemical and thermal freeze out scenario is described and the necessity of its inclusion in a hydrodynamical code is discussed. Finally, we show how to formulate continuous particle emission in hydrodynamics and discuss extensively its consistency with data. We point out in various cases that the interpretation of data is quite influenced by the choice of the particle emission mechanism.

We study, in a hydrodynamical approach, the energy dependence of the kaon mT spectra in central Pb+Pb (Au+Au) collisions. We show that the experimental data of the inverse slope parameter can be reproduced with a reasonable choice of both energy-dependent freeze-out temperature and initial conditions.

Using the hydrodynamical code NeXSPheRIO, we compare predictions as usually done in hydrodynamics, using centrality windows defined through the impact parameter, and as obtainable experimentally, using windows in participant number.