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.

We explore the effects of shear viscosity on the hydrodynamic evolution and final hadron spectra of Cu + Cu collisions at ultrarelativistic collision energies, using the newly developed (2 + 1)-dimensional viscous hydrodynamic code VISH2+1. Based on the causal Israel-Stewart formalism, this code describes the transverse evolution of longitudinally boost-invariant systems without azimuthal symmetry around the beam direction. Shear viscosity is shown to decelerate the longitudinal and accelerate the transverse hydrodynamic expansion. For fixed initial conditions, this leads to a longer quark-gluon plasma (QGP) lifetime, larger radial flow in the final state, and flatter transverse momentum spectra for the emitted hadrons compared to ideal fluid dynamic simulations. We find that the elliptic flow coefficient v 2 is particularly sensitive to shear viscosity: even the lowest value allowed by the AdS/CFT conjecture η/s 1/4π suppresses v 2 enough to have significant consequences for the phenomenology of heavy-ion collisions at the BNL Relativistic Heavy Ion Collider (RHIC). A comparison between our numerical results and earlier analytic estimates of viscous effects within a blast-wave model parametrization of the expanding fireball at freeze-out reveals that the full dynamical theory leads to much tighter constraints for the specific shear viscosity η/s, thereby supporting the notion that the quark-gluon plasma created at RHIC exhibits almost "perfect fluidity."

We compute the time evolution of elliptic flow in non-central relativistic heavy-ion collisions, using a (2+1)-dimensional code with longitudinal boost-invariance to simulate viscous fluid dynamics in the causal Israel-Stewart formulation. We show that even "minimal" shear viscosity η/s = /(4π) leads to a large reduction of elliptic flow compared to ideal fluid dynamics, raising questions about the interpretation of recent experimental data from the Relativistic Heavy Ion Collider.PACS numbers: 25.75.Ld, 47.75.+f, 12.38.Mh The success of the hydrodynamic model in describing the bulk of hadron production in Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC) [1] has led to a paradigmatic shift in our view of the quark-gluon plasma (QGP): Instead of behaving like a gas of weakly interacting quarks and gluons [2], as naively expected on the basis of asymptotic freedom in QCD, its collective properties rather reflect those of a "perfect liquid" with (almost) vanishing viscosity. However, due to quantum mechanical uncertainty no fluid can have exactly zero viscosity [3], and recent work [4] on strongly coupled gauge field theories, based on techniques exploiting the AdS/CFT correspondence, suggests an absolute lower limit for the ratio of shear viscosity η to entropy density s: η/s ≥ /4π. This raises the interesting question how close to this limit the actual value of the shear viscosity of the QGP created at RHIC is.Answering this question requires hydrodynamic simulations for relativistic viscous fluids in which the ratio η/s enters as a parameter. To study the anisotropic ("elliptic") collective flow in non-central heavy-ion collisions, from which limits on η/s can be extracted [5], requires a code that evolves the hydrodynamic fields at least in the two dimensions transverse to the heavy-ion beam. In this Letter we present our first results from such simulations [6]; a longer paper with a discussion of all technical details of our approach is in preparation [7].Relativistic hydrodynamics of viscous fluids is technically demanding. The straightforward relativistic generalization of the non-relativistic Navier-Stokes equation yields unstable equations that can lead to acausal signal propagation. A causally consistent theoretical framework was developed 30 years ago by Israel and Stewart [8]. It involves the simultaneous solution of hydrodynamic equations for a generalized energy-momentum tensor containing viscous pressure contributions, π µν (x), together with kinetic evolution equations, characterized by a (short) microscopic collision time scale τ π , for the dynamical approach of π µν towards its Navier-Stokes limit. Compared to ideal fluid dynamics, this leads effectively to more than a doubling of the number of coupled partial differential equations to be solved [9].The last couple of years have seen extensive activity in implementing the Israel-Stewart equations (and slight variations thereof) [8,9,10,11,12] numerically, for systems with boost-invariant longitudinal expansion and transverse ex...

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