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Finite Volume Evolution Galerkin Methods for the Shallow Water Equations with Dry Beds

Finite Volume Evolution Galerkin Methods for the Shallow Water Equations with Dry Beds
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Year:    2011

Author:    Andreas Bollermann, Sebastian Noelle, Maria Lukáčová-Medvid'ová

Communications in Computational Physics, Vol. 10 (2011), Iss. 2 : pp. 371–404

Abstract

We present a new Finite Volume Evolution Galerkin (FVEG) scheme for the solution of the shallow water equations (SWE) with the bottom topography as a source term. Our new scheme will be based on the FVEG methods presented in (Noelle and Kraft, J. Comp. Phys., 221 (2007)), but adds the possibility to handle dry boundaries. The most important aspect is to preserve the positivity of the water height. We present a general approach to ensure this for arbitrary finite volume schemes. The main idea is to limit the outgoing fluxes of a cell whenever they would create negative water height. Physically, this corresponds to the absence of fluxes in the presence of vacuum. Well-balancing is then re-established by splitting gravitational and gravity driven parts of the flux. Moreover, a new entropy fix is introduced that improves the reproduction of sonic rarefaction waves.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.220210.020710a

Communications in Computational Physics, Vol. 10 (2011), Iss. 2 : pp. 371–404

Published online:    2011-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    34

Keywords:   

Author Details

Andreas Bollermann

Sebastian Noelle

Maria Lukáčová-Medvid'ová

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