We develop a combined hydro-kinetic approach which incorporates a hydrodynamical expansion of the systems formed in textit{A}+textit{A} collisions and their dynamical decoupling described by escape probabilities. The method corresponds to a generaliz
ed relaxation time ($tau_{text{rel}}$) approximation for the Boltzmann equation applied to inhomogeneous expanding systems; at small $tau_{text{rel}}$ it also allows one to catch the viscous effects in hadronic component - hadron-resonance gas. We demonstrate how the approximation of sudden freeze-out can be obtained within this dynamical picture of continuous emission and find that hypersurfaces, corresponding to a sharp freeze-out limit, are momentum dependent. The pion $m_{T}$ spectra are computed in the developed hydro-kinetic model, and compared with those obtained from ideal hydrodynamics with the Cooper-Frye isothermal prescription. Our results indicate that there does not exist a universal freeze-out temperature for pions with different momenta, and support an earlier decoupling of higher $p_{T}$ particles. By performing numerical simulations for various initial conditions and equations of state we identify several characteristic features of the bulk QCD matter evolution preferred in view of the current analysis of heavy ion collisions at RHIC energies.
We show effects of granular structure of the initial conditions (IC) of hydrodynamic description of high-energy nucleus-nucleus collisions on some observables, especially on the elliptic-flow parameter v2. Such a structure enhances production of isot
ropically distributed high-pT particles, making v2 smaller there. Also, it reduces v2 in the forward and backward regions where the global matter density is smaller, so where such effects become more efficacious.
