A fully implicit wetting-drying method for DG-FEM shallow water models, with an application to the Scheldt Estuary
(2011) Computer Methods in Applied Mechanics and Engineering — Vol. 200, p. 509-524 (2011)
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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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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. Computer Methods in Applied Mechanics and Engineering, 200, 509-524. https://doi.org/10.1016/j.cma.2010.07.001 (Original work published 2011)