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
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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