J. Gerhard

Relativistic hydrodynamics on graphic cards

Abstract We show how to accelerate relativistic hydrodynamics simulations using graphic cards (graphic processing units, GPUs). These improvements are of highest relevance e.g. to the field of high-energetic nucleus–nucleus collisions at RHIC and LHC where (ideal and dissipative) relativistic hydrodynamics is used to calculate the evolution of hot and dense QCD matter. The results reported here are based on the Sharp And Smooth Transport Algorithm (SHASTA), which is employed in many hydrodynamical models and hybrid simulation packages, e.g. the Ultrarelativistic Quantum Molecular Dynamics model (UrQMD). We have redesigned the SHASTA using the OpenCL computing framework to work on accelerators like graphic processing units (GPUs) as well as on multi-core processors. With the redesign of the algorithm the hydrodynamic calculations have been accelerated by a factor 160 allowing for event-by-event calculations and better statistics in hybrid calculations.

Analytical Solutions of Landau (1+1)-Dimensional Hydrodynamics

To help guide our intuition, summarize important features, and point out essential elements, we review the analytical solutions of Landau (1+1)-dimensional hydrodynamics and exhibit the full evolution of the dynamics from the very beginning to subsequent times. Special emphasis is placed on the matching and the interplay between the Khalatnikov solution and the Riemann simple wave solution at the earliest times and in the edge regions at later times.

Longitudinal hydrodynamics from event-by-event Landau initial conditions

Here we investigate three-dimensional ideal hydrodynamic evolution, with Landau initial conditions, incorporating event-by-event variation with many events and transverse density inhomogeneities. We show that the transition to boost-invariant flow occurs too late for realistic setups, with corrections of θ (20%-30%) expected at freeze-out for most scenarios. Moreover, the deviation from boost invariance is correlated with both transverse flow and elliptic flow, with the more highly transversely flowing regions also showing the most violation of boost invariance. Therefore, if longitudinal flow is not fully developed at the early stages of heavy ion collisions, hydrodynamics where boost invariance holds at midrapidity is inadequate to extract transport coefficients of the quark-gluon plasma. We conclude by arguing that developing experimental probes of boost invariance is necessary, and suggest some promising directions in this regard.

Stability of transport models under changes of resonance parameters: A study with the ultrarelativistic quantum molecular dynamics model

The Ultrarelativistic Quantum Molecular Dynamics [UrQMD] model is widely used to simulate heavy ion collisions in broad energy ranges. It consists of various components to implement the different physical processes underlying the transport approach. A major building block are the shared tables of constants, implementing the baryon masses and widths. Unfortunately, many of these input parameters are not well known experimentally. In view of the upcoming physics program at FAIR, it is therefore of fundamental interest to explore the stability of the model results when these parameters are varied. We perform a systematic variation of particle masses and widths within the limits proposed by the particle data group (or up to 10%). We find that the model results do only weakly depend on the variation of these input parameters. Thus, we conclude that the present implementation is stable with respect to the modification of not yet well specified particle parameters.

Hydrodynamics from Landau initial conditions

We investigate ideal hydrodynamic evolution, with Landau initial conditions, both in a semi-analytical 1+1D approach and in a numerical code incorporating event-by event variation with many events and transverse density inhomogeneities. The object of the calculation is to test how fast would a Landau initial condition transition to a commonly used boost-invariant expansion. We show that the transition to boost-invariant flow occurs too late for realistic setups, with corrections of O (20 — 30%) expected at freeze out for most scenarios. Moreover, the deviation from boost-invariance is correlated with both transverse flow and elliptic flow, with the more highly transversely flowing regions also showing the most violation of boost invariance. Therefore, if longitudinal flow is not fully developed at the early stages of heavy ion collisions, 2+1 dimensional hydrodynamics is inadequate to extract transport coefficients of the quark-gluon plasma. Based on [1, 2]