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Efficient GPU implementation of a two waves WAF method for the two-dimensional one layer Shallow Water system on structured meshes

Marc de la Asuncion, Manuel J. Castro, E. D. Fernandez-Nieto, Jose M. Mantas, Sergio Ortega Acosta, Jose Manuel Gonzalez-Vida
Dpto. Lenguajes y Sistemas Informaticos, Universidad de Granada
Universidad de Granada, 2011

@article{de2011efficient,

   title={Efficient GPU implementation of a two waves WAF method for the two-dimensional one layer Shallow Water system on structured meshes},

   author={de la Asunci{‘o}na, M. and Castroc, M.J. and Fern{‘a}ndez-Nietob, ED and Mantasa, J.M. and Acostac, S.O. and Gonz{‘a}lez-Vidad, J.M.},

   year={2011}

}

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The numerical solutions of Shallow Water Equations are useful for applications related to geophysical flows that usually take place in large computational domains and could require real time calculation. Therefore, parallel versions of accurate and efficient numerical solvers for high performance platforms are needed to be able to deal with these simulation scenarios in reasonable times. In this paper we present an efficient CUDA implementation of a first and second order HLL methods and a two-waves TVD-WAF one. We propose to write all these methods under a common framework, such as, their CUDA implementations share the same structure. In particular, the reformulation of WAF numerical flux and the improved definition of the flux limiter allows us to obtain a more robust solver in situations like wet/dry fronts. Finally, some numerical tests are presented showing that WAF method is slightly slower that the rst order HLL method and twice faster than the second order HLL method, but it provides numerical results almost as accurate as the second order HLL scheme.
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