|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
Shallow water equations; Wetting–drying; Discontinuous Galerkin; Finite element method; Implicit time integration
|Auteurs|| || Top |
- Kärnä, T.
- de Brye, B.
- Gourgue, O.
- Lambrechts, J.
- Comblen, R.
- Legat, V.
- Deleersnijder, E.
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.