A MUSTA-FORCE Algorithm for Solving Partial Differential Equations of Relativistic Hydrodynamics

Joanna Porter-Sobieraj 2 , Marcin Słodkowski 1 , Daniel Kikoła 3 , Jan Sikorski 4  and Paweł Aszklar 4
  • 1 Faculty of Physics, Warsaw University of Technology, Koszykowa 75, 00-662, Warsaw, Poland
  • 2 Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662, Warsaw, Poland
  • 3 Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662, Warsaw, Poland
  • 4 Faculty of Physics, University of Warsaw, Pasteura 5, 02-093, Warsaw, Poland
Joanna Porter-Sobieraj
  • Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662, Warsaw, Poland
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, Marcin Słodkowski
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  • Faculty of Physics, Warsaw University of Technology, Koszykowa 75, 00-662, Warsaw, Poland
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, Daniel Kikoła
  • Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662, Warsaw, Poland
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, Jan Sikorski and Paweł Aszklar


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.

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The International Journal of Nonlinear Sciences and Numerical Simulation publishes original papers on all subjects relevant to nonlinear sciences and numerical simulation. The journal is directed at researchers in nonlinear sciences, engineers, and computational scientists, economists, and others, who either study the nature of nonlinear problems or conduct numerical simulations of nonlinear problems.