An implicit wetting–drying algorithm for the discontinuous Galerkin method

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.