Abstract
We compare the treatment of wetting and drying for shallow water flows at the coast using a discontinuous Galerkin (DG) scheme with classical finite volumes in one space dimension. The presented DG scheme employs piecewise linear ansatz functions and is formally second-order accurate. The core of the method is a velocity based “limiting” of the momentum, which provides stable and accurate solutions in the computation of inundation events. Artificial gradients of the water surface elevation which are introduced by the DG discretization at the wet/dry interface are specially handled to prevent spurious velocities. The finite volume method is based on second-order hydrostatic reconstruction. In general, both methods show comparable results in terms of stability and accuracy. For certain situations the DG method is slightly superior.
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Acknowledgements
The authors gratefully acknowledge support through the ASCETE (Advanced Simulation of Coupled Earthquake and Tsunami Events) project sponsored by the Volkswagen foundation and through ASTARTE—Assessment, STrategy And Risk Reduction for Tsunamis in Europe. Grant 603839, 7th FP (ENV.2013.6.4-3)
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Vater, S., Beisiegel, N., Behrens, J. (2017). Comparison of Wetting and Drying Between a RKDG2 Method and Classical FV Based Second-Order Hydrostatic Reconstruction. In: Cancès, C., Omnes, P. (eds) Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems. FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-319-57394-6_26
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