Quasi-nodal third-order Bernstein polynomials in a discontinuous Galerkin model for flooding and drying
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A quasi-nodal discontinuous Galerkin (DG) model employs monotonicity preserving Bernstein polynomials as basis functions in combination with an efficient vertex-based slope limiter. As opposed to classical nodal Lagrange DG models, it simulates flooding and drying stably even with higher than second-order basis functions. We study the viability of the latter for inundation simulations in general and discuss the quality of the new basis functions. A subsequent numerical study demonstrates the conservation properties and local convergence rates of the new method.
KeywordsDiscontinuous Galerkin Bernstein polynomials Inundation High-order methods
The authors gratefully acknowledge support through the Cluster of Excellence ‘CliSAP’ (EXC177), University of Hamburg, funded through the German Science Foundation (DFG), as well as through ASTARTE—Assessment, STrategy And Risk Reduction for Tsunamis in Europe. Grant 603839, 7th FP (ENV.2013.6.4-3). The second author also acknowledges support through Advanced Simulation of Coupled Earthquake and Tsunami Events (ASCETE) funded by the Volkswagen foundation. Furthermore, the authors would like to thank the anonymous reviewers for their kind consideration and comments that helped improve the manuscript.
- Aizinger V (2011) A geometry independent slope limiter for the discontinuous Galerkin method. Comput Sci High Perform Comput IV NNFM 115:207–217Google Scholar
- Hesthaven JS, Warburton T (2008) Nodal discontinuous Galerkin methods: algorithms, analysis, and applications. Springer, BerlinGoogle Scholar
- Hindenlang F, Gassner G, Bolemann T, Munz CD (2010) Unstructured high order grids and their application in discontinuous Galerkin methods. Preprint Series, Stuttgart Research Centre for Simulation Technology (SRC SimTech) issue no, pp 2010-26Google Scholar
- Rusanov VV (1962) Calculation of interaction of non-steady shock waves with obstacles. NRC, Division of Mechanical EngineeringGoogle Scholar
- Toro EF (2001) Shock capturing methods for free-surface shallow flows. Wiley, New YorkGoogle Scholar
- Vater S (2013) A multigrid-based multiscale numerical scheme for shallow water flows at low Froude number. PhD thesis, Freie Universität Berlin. http://www.diss.fu-berlin.de/diss/receive/FUDISS_thesis_000000093897
- Vater S, Beisiegel N, Behrens J (2015) A limiter-based well-balanced discontinuous Galerkin method for shallow-water flows with wetting and drying: one-dimensional case. Advances in Water Resources Under reviewGoogle Scholar
- Westerink JJ, Luettich RA, Feyen JC, Atkinson JH, Dawson C, Roberts HJ, Powell MD, Dunion JP, Kubatko EJ, Pourtaheri H (2008) A basin- to channel-scale unstructured grid hurricane storm surge model applied to Southern Louisiana. Mon Weather Rev 136:833–864. doi: 10.1175/2007MWR1946.1 CrossRefGoogle Scholar