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

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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.

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Acknowledgements

The PhD fellowship of Hoang-Anh Le is provided by the Université catholique de Louvain, Belgium. This research has been conducted under the framework of CARE - Rescif, Vietnam’s initiative with Grant number Tc-TTC-2017-08. Computational resources have been provided by the Consortium des Équipements de Calcul Intensif (CÉCI), funded by the Fonds de la Recherche Scientifique de Belgique (F.R.S.-FNRS) under Grant No. 2.5020.11. E. Deleersnijder and S. Soares-Frazão are honorary research associates with F.R.S.-FNRS.

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Authors and Affiliations

  1. Institute of Mechanics, Materials and Civil Engineering (IMMC), Université Catholique de Louvain, Place du Levant 1, 1348, Louvain-la-Neuve, Belgium

    Hoang-Anh Le, Jonathan Lambrechts, Eric Deleersnijder & Sandra Soares-Frazão

  2. Asian Research Center on Water (CARE-Rescif), Ho Chi Minh City University of Technology, Block B7, 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City, Vietnam

    Hoang-Anh Le & Nicolas Gratiot

  3. FB 10, Institut für Mathematik, Universität Kassel, Heinrich-Plett-Straße 40, 34132, Kassel, Germany

    Sigrun Ortleb

  4. CNRS, IRD, Grenoble INP, IGE, Université Grenoble Alpes, 38000, Grenoble, France

    Nicolas Gratiot

  5. Earth and Life Institute (ELI), Université Catholique de Louvain, Avenue Georges Lemaître 4, 1348, Louvain-la-Neuve, Belgium

    Eric Deleersnijder

  6. Delft Institute of Applied Mathematics (DIAM), Delft University of Technology, Van Mourik Broekmanweg 6, 2628XE, Delft, The Netherlands

    Eric Deleersnijder

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  1. Hoang-Anh Le
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Le, HA., Lambrechts, J., Ortleb, S. et al. An implicit wetting–drying algorithm for the discontinuous Galerkin method: application to the Tonle Sap, Mekong River Basin. Environ Fluid Mech 20, 923–951 (2020). https://doi.org/10.1007/s10652-019-09732-7

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