17293

Non-Hydrostatic Pressure Shallow Flows: GPU Implementation Using Finite-Volume and Finite-Difference Scheme

C. Escalante, T. Morales de Luna, M.J. Castro
Departamento de Analisis Matematico, Estadistica e Investigacion Operativa, y Matematica Aplicada, Universidad de Malaga, Spain
arXiv:1706.04551 [math.NA], (14 Jun 2017)

@article{escalante2017nonhydrostatic,

   title={Non-Hydrostatic Pressure Shallow Flows: GPU Implementation Using Finite-Volume and Finite-Difference Scheme},

   author={Escalante, C. and Luna, T. Morales de and Castro, M.J.},

   year={2017},

   month={jun},

   archivePrefix={"arXiv"},

   primaryClass={math.NA}

}

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We consider the depth-integrated non-hydrostatic system derived by Yamazaki et al. An efficient formally second-order well-balanced hybrid finite volume/difference numerical scheme is proposed. The scheme consists in a two-step algorithm. First, the hyperbolic part of the system is discretized using a PVM path-conservative finite-volume method. Second, the dispersive terms are solved by means of compact finite differences. A new methodology is also presented to handle wave breaking over complex bathymetries. This adapts well to GPU-architectures and guidelines about its GPU implementation are introduced. The method has been applied to idealized and challenging experimental test cases, which shows the efficiency and accuracy of the method.
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