A Discontinuous Galerkin Method for Non-hydrostatic Shallow Water Flows

Jeschke, Anja; Vater, Stefan; Behrens, Jörn

doi:10.1007/978-3-319-57394-6_27

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A Discontinuous Galerkin Method for Non-hydrostatic Shallow Water Flows

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Jeschke, A., Vater, S., & Behrens, J. (2017). A Discontinuous Galerkin Method for Non-hydrostatic Shallow Water Flows. In C. Cancès, & P. Omnes (Eds.), Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems (pp. 247-255). Cham: Springer International Publishing.

Cite as: https://hdl.handle.net/21.11116/0000-0001-7E59-F

Abstract

In this workBehrens, Jörn a non-hydrostatic depth-averagedJeschke, Anja shallow water model is discretized using the discontinuous Galerkin (DG) Vater, Stefan 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.