An implicit wetting–drying algorithm for the discontinuous Galerkin method
Application to the Tonle Sap, Mekong River Basin
Hoang Anh Le (Ho Chi Minh City University of Technology (HCMUT), Université Catholique de Louvain)
Jonathan Lambrechts (Université Catholique de Louvain)
Sigrun Ortleb (University of Kassel)
Nicolas Gratiot (Ho Chi Minh City University of Technology (HCMUT), Université Grenoble Alpes)
Eric Deleersnijder (TU Delft - Mathematical Physics, TU Delft - Delft Institute of Applied Mathematics, Université Catholique de Louvain)
Sandra Soares-Frazão (Université Catholique de Louvain)
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Abstract
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.