Lagrange-Eulerian method for numerical integration of the gas dynamics equations: parallel implementation on GPUs

Abstract: We describe a new CSPH-TVD method for numerical integration of hydrodynamical equations. The method is based on combined Lagrange-Euler approaches, and it has been devoted to simulations of hydrodynamical flows in various astrophysical systems with non-homogeneous gravitational fields and the non-steady boundary between gas and vacuum. A numerical algorithm was tested on analytical solutions for various problems, and a detailed comparison of our method with the MUSCL scheme is also presented in the paper. It is shown that the CSPH-TVD scheme has a second order of accuracy for smooth solutions (well-balanced approach) and it provides reliable solutions in the vicinity of strong shock waves and at the open gas-vacuum interfaces. We also study the effectiveness of parallel implementations of CSPH-TVD method for various NVIDIA Tesla K20/40/80, P100 graphics processors.