Simulation and visualization of the Saint-Venant system using GPUs |
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Authors: | André R Brodtkorb Trond R Hagen Knut-Andreas Lie Jostein R Natvig |
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Affiliation: | 1. Dept. Appl. Math., SINTEF ICT, P.O. Box 124, Blindern, 0314, Oslo, Norway
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Abstract: | We consider three high-resolution schemes for computing shallow-water waves as described by the Saint-Venant system and discuss
how to develop highly efficient implementations using graphical processing units (GPUs). The schemes are well-balanced for
lake-at-rest problems, handle dry states, and support linear friction models. The first two schemes handle dry states by switching
variables in the reconstruction step, so that bilinear reconstructions are computed using physical variables for small water
depths and conserved variables elsewhere. In the third scheme, reconstructed slopes are modified in cells containing dry zones
to ensure non-negative values at integration points. We discuss how single and double-precision arithmetics affect accuracy
and efficiency, scalability and resource utilization for our implementations, and demonstrate that all three schemes map very
well to current GPU hardware. We have also implemented direct and close-to-photo-realistic visualization of simulation results
on the GPU, giving visual simulations with interactive speeds for reasonably-sized grids. |
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