Repository: Freie Universität Berlin, Math Department

A Discontinuous Galerkin Method for Non-hydrostatic Shallow Water Flows

Jeschke, A. and Vater, S. and Behrens, J. (2017) A Discontinuous Galerkin Method for Non-hydrostatic Shallow Water Flows. In: Finite Volumes for Complex Applications VIII -- Hyperbolic, Elliptic and Parabolic Problems. Springer, pp. 247-255. ISBN Print: 978-3-319-57393-9 Online: 978-3-319-57394-6

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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.

Item Type:Book Section
Additional Information:FVCA 8, Lille, France, June 2017
Uncontrolled Keywords:Shallow water equations Non-hydrostatic Discontinuous galerkin method
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group
ID Code:2413
Deposited By: Ulrike Eickers
Deposited On:25 Feb 2020 15:06
Last Modified:25 Feb 2020 15:11

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