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High-Order Schemes for the Shallow Water Equations on GPUs
Norwegian University of Science and Technology, Faculty of Information Technology, Mathematics and Electrical Engineering, Department of Computer and Information Science.
2013 (English)MasteroppgaveStudent thesis
Abstract [en]

In this thesis, well-balanced, central-upwind high-resolution methods of high order are developed for the two-dimensional shallow water equations, on the graphics processing unit (GPU). The methods are based on a fifth-order Weighted Essentially Non-Oscillating (WENO) reconstruction technique and a fourth-order Gaussian quadrature for the one-sided interface fluxes. Two schemes are implemented, one with bilinear interpolation of the bottom topography and a second-order quadrature for the bed slope source term, and one with a fourth-order source term quadrature and a fifth-order hydrostatic WENO reconstruction of the water height. The high-order schemes are compared to a second-order scheme by Kurganov and Petrova, which recently has been implemented on the GPU by Brodtkorb. The schemes are shown to be well-balanced and are capable of outperforming the second-order scheme on smooth problems provided that dry states and discontinuities do not occur. The performance gain is larger after a low number of time steps, where speed-ups by a factor between 3 and 8 are documented. As the system evolves, the accuracy of the high-order methods drops, and the performance gain is reduced to a factor around 1.5. The schemes do, however, not support outflow and inflow boundary conditions, and are not yet tested on real-world problems. The high-order scheme using the hydrostatic reconstruction and a fourth-order source term quadrature is implemented in such a way that an extension to quadratures and reconstructions of even higher order, should be fairly straight forward.

Place, publisher, year, edition, pages
Institutt for matematiske fag , 2013. , 103 p.
URN: urn:nbn:no:ntnu:diva-20783Local ID: ntnudaim:8564OAI: diva2:618492
Available from: 2013-04-28 Created: 2013-04-28 Last updated: 2013-06-22Bibliographically approved

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