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A fully implicit wetting–drying method for DG-FEM shallow water models, with an application to the Scheldt Estuary
Kärnä, T.; de Brye, B.; Gourgue, O.; Lambrechts, J.; Comblen, R.; Legat, V.; Deleersnijder, E. (2011). A fully implicit wetting–drying method for DG-FEM shallow water models, with an application to the Scheldt Estuary. Comput. methods appl. mech. eng. 200(5-8): 509-524. dx.doi.org/10.1016/j.cma.2010.07.001
In: Computer Methods in Applied Mechanics and Engineering. Elsevier: Amsterdam. ISSN 0045-7825; e-ISSN 1879-2138, meer
Peer reviewed article  
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Trefwoord
    Marien/Kust
Author keywords
    Shallow water equations; Wetting–drying; Discontinuous Galerkin; Finite element method; Implicit time integration
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Abstract
    Resolving the shoreline undulation due to tidal excursion is a crucial part of modelling water flow in estuaries and coastal areas. Nevertheless, maintaining positive water column depth and numerical stability has proved out to be a very difficult task that requires special attention. In this paper we propose a novel wetting–drying method in which the position of the sea bed is allowed to fluctuate in drying areas. The method is implemented in a Discontinuous Galerkin Finite Element Model (DG-FEM). Unlike most methods in the literature our method is compatible with fully implicit time-marching schemes, thus reducing the overall computational cost significantly. Moreover, global and local mass conservation is guaranteed which is crucial for long-term environmental applications. In addition consistency with tracer equation is also ensured. The performance of the proposed method is demonstrated with a set of test cases as well as a real-world application to the Scheldt Estuary. Due to the implicit time integration, the computational cost in the Scheldt application is reduced by two orders of magnitude. Although a DG-FEM implementation is presented here, the wetting–drying method is applicable to a wide variety of shallow water models.
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