Relativistic hydrodynamics on graphics processing units

Abstract: Hydrodynamics calculations have been successfully used in studies of the bulk properties of the Quark-Gluon Plasma, particularly of elliptic flow and shear viscosity. However, there are areas (for instance event-by-event simulations for flow fluctuations and higher-order flow harmonics studies) where further advancement is hampered by lack of efficient and precise 3+1D~program. This problem can be solved by using Graphics Processing Unit (GPU) computing, which offers unprecedented increase of the computing power compared to standard CPU simulations. In this work, we present an implementation of 3+1D ideal hydrodynamics simulations on the Graphics Processing Unit using Nvidia CUDA framework. MUSTA-FORCE (MUlti STAge, First ORder CEntral, with a~slope limiter and MUSCL reconstruction) and WENO (Weighted Essentially Non-Oscillating) schemes are employed in the simulations, delivering second (MUSTA-FORCE), fifth and seventh (WENO) order of accuracy. Third order Runge-Kutta scheme was used for integration in the time domain. Our implementation improves the performance by about 2~orders of magnitude compared to a~single threaded program. The algorithm tests of 1+1D~shock tube and 3+1D~simulations with ellipsoidal and Hubble-like expansion are presented.