Abstract
We consider the Saint Venant system (shallow water equations), i.e. an approximation of the incompressible Euler equations widely used to describe river flows, flooding phenomena or erosion problems. We focus on problems involving dry-wet transitions and propose a solution technique using the Spectral Element Method (SEM) stabilized with a variant of the Entropy Viscosity Method (EVM) that is adapted to treat dry zones.
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Acknowledgements
This work is partly supported by the National Science Foundation grants DMS-1015984 and DMS-1217262 and by the Air Force Office of Scientific Research, USAF, under grant/contract number FA99550-12-0358. It is also supported by grants of the French research agency (ANR project MEDIMAX).
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Pasquetti, R., Guermond, J.L., Popov, B. (2015). Stabilized Spectral Element Approximation of the Saint Venant System Using the Entropy Viscosity Technique. In: Kirby, R., Berzins, M., Hesthaven, J. (eds) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014. Lecture Notes in Computational Science and Engineering, vol 106. Springer, Cham. https://doi.org/10.1007/978-3-319-19800-2_36
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DOI: https://doi.org/10.1007/978-3-319-19800-2_36
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-19799-9
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