A Discontinuous Galerkin Method for Non-hydrostatic Shallow Water Flows

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 200)


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.


Shallow water equations Non-hydrostatic Discontinuous galerkin method 

MSC (2010):

65M08 35Q86 86-08 



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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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversität HamburgHamburgGermany

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