Accelerating Euler equations numerical solver on graphics processing units Pierre Kestener 1 , Fr´ ed´ eric Chˆ ateau 1 , Romain Teyssier 2 1 CEA, Centre de Saclay, DSM/IRFU/SEDI, F-91191 Gif-Sur-Yvette, France pierre.kestener@cea.fr, WWW home page: http://irfu.cea.fr/en/index.php 2 CEA, Centre de Saclay, DSM/IRFU/SAp, F-91191 Gif-Sur-Yvette, France Abstract. Finite volume numerical methods have been widely stud- ied, implemented and parallelized on multiprocessor systems or on clus- ters. Modern graphics processing units (GPU) provide architectures and new programing models that enable to harness their large processing power and to design computational fluid dynamics simulations at both high performance and low cost. We report on solving the 2D compress- ible Euler equations on modern Graphics Processing Units (GPU) with high-resolution methods, i.e. able to handle complex situations involv- ing shocks and discontinuities. We implement two different second order numerical schemes, a Godunov-based scheme with quasi-exact Riemann solver and a fully discrete second-order central scheme as originally pro- posed by Kurganov and Tadmor. Performance measurements show that these two numerical schemes can achieves x30 to x70 speed-up on recent GPU hardware compared to a mono-thread CPU reference implementa- tion. These first results provide very promising perpectives for designing a GPU-based software framework for applications in computational as- trophysics by further integrating MHD codes and N-body simulations. 1 Introduction We report on implementing different numerical schemes for solving the Euler equations on massively parallel architectures available today in graphics cards hardware. Euler equations govern inviscid flow and are the fundamental basis of most computational fluid dynamics (CFD) problems, which often require large computing resources due to the dimensions of the domain (space and time). Mod- ern GPU provide efficient cost-effective computing power to potentially solve large problems and prepare for running on capability supercomputer. The pur- pose of this paper is to show one can efficiently perform high-order numerical schemes simulations of Euler equations on a single GPU system. GPU used to be graphics tasks dedicated co-processors. Before the advent of the Nvidia CUDA architecture (2006), some deep knowledge of the graphics pipeline model and low-level architecture was required to adapt a CPU code to run on the GPU. In 2005, Hagen et al. [1] implemented the Lax-Friedrichs Euler solver using the graphics pipeline approach, and designed shaders programs in