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Efficient Implementation of the CPR Formulation for the Navier-Stokes Equations on GPUs

Malte Hoffmann, Claus-Dieter Munz, Z. J. Wang
Institute of Aerodynamics and Gas Dynamics, University of Stuttgart, Pfaffenwaldring 21, 70569, Germany
Seventh International Conference on Computational Fluid Dynamics (ICCFD7), 2012

@article{hoffmann2012efficient,

   title={Efficient Implementation of the CPR Formulation for the Navier-Stokes Equations on GPUs},

   author={Hoffmann, M. and Munz, C.D. and Wang, ZJ},

   year={2012}

}

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The correction procedure via reconstruction (CPR) formulation for the Euler and Navier-Stokes equations is implemented on a NVIDIA graphics processing unit (GPU) using CUDA C with both explicit and implicit time-stepping schemes for 2D unstructured triangular grids. For the implicit time integration, a first order time approximation with Newton iteration and Gauy elimination is used to solve the system of equations, while for explicit time-stepping a 3-stage Runge-Kutta scheme is used. For the implicit time-stepping on the GPU a preconditioned mesh coloring algorithm is developed, which is derived from the Four Color Theorem known from the graph theory. For the speed-up, compared to a single core of an Intel Xeon CPU, a factor up to 112-130 for explicit time-stepping is achieved, varying on the polynomial degree k and the chosen numerical flow. For the implicit time-stepping the maximum speed-up is between 47 and 89. All calculations are made in double precision using a single NVIDIA Tesla C2050.
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