Dense bulk matter is formed during heavy-ion collision and expands towards a vacuum. It behaves as a perfect fluid, described by relativistic hydrodynamics. In order to study initial condition fluctuation and properties of jet propagation in dense hot matter, we assume a Cartesian laboratory frame with several million cells in a stencil with high-accuracy data volume grids. Employing numerical algorithms to solve hydrodynamic equations in such an assumption requires a lot of computing power. Hydrodynamic simulations of nucleus + nucleus interactions in the range of energies of the Large Hadron Collider (LHC) are carried out using our program, which uses Graphics Processing Units (GPUs) and Compute Unified Device Architecture (CUDA). In this work, we focused on transforming hydrodynamic quantities into kinetic descriptions. We implemented the hypersurface freeze-out conditions using marching cubes techniques. We developed freeze-out procedures to obtain the momentum distributions of particles on the hypersurface. The final particle distributions, elliptic flow, and higher harmonics are comparable to the experimental LHC data.

Understanding event-by-event correlations and fluctuations is crucial for the comprehension of the dynamics of heavy ion collisions. Relativistic hydrodynamics is an elegant tool for modelling these phenomena; however, such simulations are time-consuming, and conventional CPU calculations are not suitable for event-by-event calculations. This work presents a feasibility study of a new hydrodynamic code that employs graphics processing units together with a general MUSTA-FORCE algorithm (Multi-Stage Riemann Algorithm – First-Order Centred Scheme) to deliver a high-performance yet universal tool for event-by-event hydrodynamic simulations. We also investigate the performance of selected slope limiters that reduce the amount of numeric oscillations and diffusion in the presence of strong discontinuities and shock waves. The numerical results are compared to the exact solutions to assess the code’s accuracy.

We are developing a software for energy loss simulation which is affected by jets in the nuclear matter described by relativistic hydrodynamics. Our program uses a Cartesian coordinate system in order to provide high spatial resolution for the analysis of jets propagation in nuclear matter. In this work, we use 7th order WENO numerical algorithm which is resistant to numerical oscillations and diffusions. For simulating energy losses in the bulk nuclear medium, we develop efficient hydrodynamic simulation program for parallel computing using Graphics Processing Unit (GPU) and Compute Unified Device Architecture (CUDA). It allows us to prepare event-by-event simulations in high computing precision in order to study jet modifications in the medium and event-by-event simulations of fluctuating initial conditions. In our simulation, we start the hydrodynamic simulation from generation initial condition based on the UrQMD model in order to simulate comparable nucleus-nucleus interaction in the RHIC and LHC energies. The main part of this simulation is the computation of hydrodynamic system evolution. We present obtained energy density distributions which can be compared to experimental results.