Abstract
In this work a non-hydrostatic depth-averaged shallow water model is discretized using the discontinuous Galerkin (DG) Method. The model contains a non-hydrostatic pressure component, similar to Boussinesq-type equations, which allows for dispersive gravity waves. The scheme is a projection method and consists of a predictor step solving the hydrostatic shallow water equations by the Runge-Kutta DG method. In the correction the non-hydrostatic pressure component is computed by satisfying a divergence constraint for the velocity. This step is discretized by application of the DG discretization to the first order elliptic system. The numerical tests confirm the correct dispersion behavior of the method, and show its validity for simple test cases.
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Acknowledgements
The authors A.J. and J.B. want to thank the European Union, who funded this work within the project ASTARTE—Assessment, Strategy And Risk Reduction for Tsunamis in Europe—FP7-ENV2013 6.4-3, Grant 603839. The authors J.B. and S.V. acknowledge additional support through the ASCETE project, funded by the Volkswagen Foundation.
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Jeschke, A., Vater, S., Behrens, J. (2017). A Discontinuous Galerkin Method for Non-hydrostatic Shallow Water Flows. In: Cancès, C., Omnes, P. (eds) Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems. FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-319-57394-6_27
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