An implicit wetting–drying algorithm for the discontinuous Galerkin method: application to the Tonle Sap, Mekong River Basin

• Published in: Environmental fluid mechanics (Dordrecht, Netherlands : 2001) Vol. 20; no. 4; pp. 923 - 951
• Main Authors: Le, Hoang-Anh, Lambrechts, Jonathan, Ortleb, Sigrun, Gratiot, Nicolas, Deleersnijder, Eric, Soares-Frazão, Sandra
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01-08-2020; Springer Nature B.V; Springer Verlag
• Subjects: Algorithms; Classical Mechanics; Coastal flooding; Coastal zone; Coastal zones; Computer simulation; Conservation; Dimensions; Drying; Earth and Environmental Science; Earth Sciences; Environmental Physics; Environmental Sciences; Finite element method; Floodplains; Galerkin method; Hydrodynamics; Hydrogeology; Hydrology/Water Resources; Interfaces; Lakes; Mathematical models; Mathematics; Ocean models; Oceanography; Oceans; Order parameters; Original Article; Rainy season; River basins; Rivers; Shallow water; Shallow water equations; Water depth; Water levels; Wet season; Wetting; Mekong River; Tonle Sap lake; DG-FEM; Mekong; SLIM; Wetting–drying; Numerical model
• ISSN: 1567-7419; 1573-1510
• DOI: 10.1007/s10652-019-09732-7

The accurate simulation of wetting–drying processes in floodplains and coastal zones is a challenge for hydrodynamic modelling, especially for long time simulations. Indeed, dedicated numerical procedures are generally time-consuming, instabilities can occur at the wet/dry front, rapid transition of wet/dry interface and mass conservation are not always ensured. We present the extension of an existing wetting–drying algorithm in two space dimensions and its application to a real case. The wetting–drying algorithm is implemented in Second-generation Louvain-la-Neuve Ice-ocean Model (
www.slim-ocean.be
), a discontinuous Galerkin finite element model solving the shallow water equations in a fully implicit way. This algorithm consists in applying a threshold value of fluid depth for a thin layer and a blending parameter in order to guarantee positive values of the water depth, while preserving local mass conservation and the well balanced property at wet/dry interfaces. The technique is first validated against standard analytical test cases (Balzano 1, Balzano 3 and Thacker test cases) and is subsquently applied in a realistic domain, the Tonle Sap Lake in the Mekong River Basin, where the water level can vary by about 10 m between the dry and the wet season.