Complete PISO and SIMPLE solvers on Graphics Processing Units

Tadeusz Tomczak, Katarzyna Zadarnowska, Zbigniew Koza, Maciej Matyka, Aukasz Miroslaw
Institute of Computer Science, Control and Robotics, Wroc law University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland
arXiv:1207.1571v1 [cs.DC] (6 Jul 2012)


   author={Tomczak}, T. and {Zadarnowska}, K. and {Koza}, Z. and {Matyka}, M. and {Miros{l}aw}, {^A}.},

   title={"{Complete PISO and SIMPLE solvers on Graphics Processing Units}"},

   journal={ArXiv e-prints},




   keywords={Computer Science – Distributed, Parallel, and Cluster Computing},




   adsnote={Provided by the SAO/NASA Astrophysics Data System}


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We implemented the pressure-implicit with splitting of operators (PISO) and semi-implicit method for pressure-linked equations (SIMPLE) solvers of the Navier-Stokes equations on Fermi-class graphics processing units (GPUs) using the CUDA technology. We also introduced a new format of sparse matrices optimized for performing elementary CFD operations, like gradient or divergence discretization, on GPUs. We verified the validity of the implementation on several standard, steady and unsteady problems. Computational effciency of the GPU implementation was examined by comparing its double precision run times with those of essentially the same algorithms implemented in OpenFOAM. The results show that a GPU (Tesla C2070) can outperform a server-class 6-core, 12-thread CPU (Intel Xeon X5670) by a factor of 4.2.
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