The iEBE-VISHNU code package performs event-by-event simulations for relativistic heavy-ion collisions using a hybrid approach based on (2+1)-dimensional viscous hydrodynamics coupled to a hadronic cascade model. We present the detailed model implementation, accompanied by some numerical code tests for the package. iEBE-VISHNU forms the core of a general theoretical framework for model-data comparisons through large scale Monte-Carlo simulations. A numerical interface between the hydrodynamically evolving medium and thermal photon radiation is also discussed. This interface is more generally designed for calculations of all kinds of rare probes that are coupled to the temperature and flow velocity evolution of the bulk medium, such as jet energy loss and heavy quark diffusion. It is impossible to use external probes to study the properties of the quark-gluon plasma (QGP), a novel state of matter created during the collisions. Experiments can only measure the momentum information of stable hadrons, who are the remnants of the collisions. In order to extract the thermal and transport properties of the QGP, one needs to rely on Monte-Carlo event-by-event model simulations, which reverse-engineer the experimental measurements to the early time dynamics of the relativistic heavy-ion collisions. Solution method: Relativistic heavy-ion collisions contain multiple stages of evolution. The physics that governs each stage is implemented into individual code component. A general driver script glues all the modular packages as a whole to perform large-scale Monte-Carlo simulations. The final results are stored into SQLite database, which supports standard querying for massive data analysis. By tuning transport coefficients of the QGP as free parameters, e.g. the specific shear viscosity η/s, we can constrain various transport properties of the QGP through model-data comparisons. Keywords Running time:The following running time is tested on a laptop computer with a 2.4 GHz Intel Core i5 CPU, 4GB memory. All the C++ and Fortran codes are compiled with the GNU Compiler Collection (GCC) 4.9.2 and -O3 optimization.

Heavy-ion collisions create deformed quark-gluon plasma (QGP) fireballs which explode anisotropically. The viscosity of the fireball matter determines its ability to convert the initial spatial deformation into momentum anisotropies that can be measured in the final hadron spectra. A quantitatively precise empirical extraction of the QGP viscosity thus requires a good understanding of the initial fireball deformation. This deformation fluctuates from event to event, and so does the finally observed momentum anisotropy. We present a harmonic decomposition of the initial fluctuations in shape and orientation of the fireball and perform event-by-event (2+1)-dimensional ideal fluid dynamical simulations to extract the resulting fluctuations in the magnitude and direction of the corresponding harmonic components of the final anisotropic flow at midrapidity. The final harmonic flow coefficients are found to depend non-linearly on the initial harmonic eccentricity coefficients. We show that, on average, initial density fluctuations suppress the buildup of elliptic flow relative to what one obtains from a smooth initial profile of the same eccentricity, and discuss implications for the phenomenological extraction of the QGP shear viscosity from experimental elliptic flow data.

Event-by-event fluctuations in the initial density distributions of the fireballs created in relativistic heavy-ion collisions lead to event-by-event fluctuations of the final anisotropic flow angles, and density inhomogeneities in the initial state cause these flow angles to vary with the transverse momentum of the emitted particles. It is shown that these effects lead to characteristically different transverse momentum dependencies for anisotropic flow coefficients extracted from different experimental methods. These differences can be used to experimentally constrain flow angle fluctuations in the final state of heavy-ion collisions which, in turn, are sensitive to the initial state density fluctuations and the shear viscosity of the expanding fireball medium.

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We show that in hydrodynamic simulations for relativistic heavy-ion collisions, strong resonance decay calculations can be performed with fewer species of particle resonances while preserving good accuracy in single particle spectra and flow anisotropies. Such partial resonance calculations boost computation efficiency by a factor of 10 which is essential for large scale event-by-event simulations.

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The iEBE-VISHNU code package performs event-by-event simulations for relativistic heavy-ion collisions using a hybrid approach based on (2+1)-dimensional viscous hydrodynamics coupled to a hadronic cascade model. We present the detailed model implementation, accompanied by some numerical code tests for the package. iEBE-VISHNU forms the core of a general theoretical framework for model-data comparisons through large scale Monte-Carlo simulations. A numerical interface between the hydrodynamically evolving medium and thermal photon radiation is also discussed. This interface is more generally designed for calculations of all kinds of rare probes that are coupled to the temperature and flow velocity evolution of the bulk medium, such as jet energy loss and heavy quark diffusion.

With the new viscous hydrodynamic + hadron cascade hybrid code VISHNU, a rather precise (O(25%)) extraction of the QGP shear viscosity (η/s) QGP from heavy-ion elliptic flow data is possible if the initial eccentricity of the collision fireball is known with < 5% accuracy. At this point, eccentricities from initial state models differ by up to 20%, leading to an O(100%) uncertainty for (η/s) QGP . It is shown that a simultaneous comparison of elliptic and triangular flow, v 2 and v 3 , puts strong constraints on initial state models and can largely eliminate the present uncertainty in (η/s) QGP . The variation of the differential elliptic flow v 2 (p T ) for identified hadrons between RHIC and LHC energies provides additional tests of the evolution model.Prologue -how to measure (η/s) QGP : Hydrodynamics converts the initial spatial deformation of the fireball created in relativistic heavy-ion collisions into final state momentum anisotropies. Viscosity degrades the conversion efficiency ε x = y 2 −x 2 y 2 +x 2