Implementation of algorithms for relativistic hydrodynamics using graphics processing units in CUDA framework

Jan Sikorski
Faculty of Physics, Warsaw University of Technology
Warsaw University of Technology, 2013


   title={Implementation of algorithms for relativistic hydrodynamics using graphics processing units in CUDA framework},

   author={Sikorski, Jan},



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Relativistic hydrodynamics became a very useful tool in high-energy physics after Landau’s application of this theory for explaining data on proton-proton collisions. It’s later application to heavy ion collisions has been very successful in modeling apparent collective behaviour of hot matter produced in such collisions. This work is a part of an effort of the hydro group at University of Warsaw to create an efficient and robust software tool for solving the equations of relativistic hydrodynamics, designed to be used by the high-energy physics community. Event-by-event calculations, which became a popular field of study recently, require many simulations to be performed. Because of that performance may become a considerable issue. As a result of this master’s thesis a number of numerical algorithms dedicated to solving conservative field equations have been implemented and tested. Especially the Weno schemes proved to be quite efficient and robust. A variety of slope limiting methods have been compared with a Musta-Force algorithm. The implementation is designed to run efficiently on contemporary graphics processing units, which have many times more computing power compared to ordinary processors. Benchmarks and comparison to an equivalent implementation of some of these algorithms in C shown speedups of over 2 orders of magnitude.
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