Hybrid approaches based on relativistic hydrodynamics and transport theory have been successfully applied for many years for the dynamical description of heavy ion collisions at ultrarelativistic energies. In this work a new viscous hybrid model empl
oying the hadron transport approach UrQMD for the early and late non-equilibrium stages of the reaction, and 3+1 dimensional viscous hydrodynamics for the hot and dense quark-gluon plasma stage is introduced. This approach includes the equation of motion for finite baryon number, and employs an equation of state with finite net-baryon density to allow for calculations in a large range of beam energies. The parameter space of the model is explored, and constrained by comparison with the experimental data for bulk observables from SPS and the phase I beam energy scan at RHIC. The favored parameter values depend on energy, but allow to extract the effective value of the shear viscosity coefficient over entropy density ratio $eta/s$ in the fluid phase for the whole energy region under investigation. The estimated value of $eta/s$ increases with decreasing collision energy, which may indicate that $eta/s$ of the quark-gluon plasma depends on baryochemical potential $mu_B$.
Many models of heavy ion collisions employ relativistic hydrodynamics to describe the system evolution at high densities. The Cooper-Frye formula is applied in most of these models to turn the hydrodynamical fields into particles. However, the number
of particles obtained from the Cooper-Frye formula is not always positive-definite. Physically negative contributions of the Cooper-Frye formula are particles that stream backwards into the hydrodynamical region. We quantify the Cooper-Frye negative contributions in a coarse-grained transport approach, which allows to compare them to the actual number of underlying particles crossing the transition hypersurface. It is found that the number of underlying inward crossings is much smaller than the one the Cooper-Frye formula gives under the assumption of equilibrium distribution functions. The magnitude of Cooper-Frye negative contributions is also investigated as a function of hadron mass, collision energy in the range $E_{rm lab} = 5-160A$ GeV, and collision centrality. The largest negative contributions we find are around 13% for the pion yield at midrapidity at $E_{rm lab} = 20A$ GeV collisions.
Following the experimental program at BNL RHIC, we perform a similar energy scan using 3+1D viscous hydrodynamics coupled to the UrQMD hadron cascade, and study the collision energy dependence of pion and kaon rapidity distributions and $m_T$-spectra
, as well as charged hadron elliptic flow. To this aim the equation of state for finite baryon density from a Chiral model coupled to the Polyakov loop is employed for hydrodynamic stage. 3D initial conditions from UrQMD are used to study gradual deviation from boost-invariant scaling flow. We find that the inclusion of shear viscosity in the hydrodynamic stage of evolution consistently improves the description of the data for Pb-Pb collisions at CERN SPS, as well as of the elliptic flow measurements for Au-Au collisions in the Beam Energy Scan (BES) program at BNL RHIC. The suggested value of shear viscosity is $eta/sge0.2$ for $sqrt{s_{NN}}=6.3dots39$ GeV.
