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DraouiEtAl_RiverFlow2022.pdf
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The 1D Saint-Venant equations are widely used in river modeling for engineering applications. The governing equations maybe formulated in several ways. In discrete form, those formulations are not equivalent. Thus, choosing the convenient intermediate variables for the conservation equations allows optimal stability with minor numerical adjustment. Two different issues should be carefully dealt with in realistic domains: the relative paucity of geometric data and the connection to larger water bodies. Regarding the data interpolation, in the absence of a precise representation of the river bed evolution, we suggest using a general datum for data definition and interpolation along the river, allowing a smooth, stable source term. As for the connection to a 2D model, an implicit boundary-connected coupling based on flux continuity is adopted. The modules above are implemented in the framework of a discontinuous Galerkin finite-element model (SLIM, www.slim-ocean.be). Validation is first performed on idealized configurations. Then, the river-delta continuum of the Mahakam River (Borneo, Indonesia) is modeled, and the results are compared to the measured water level.
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Draoui, I., Lambrechts, J., Legat, V., & Deleersnijder, E. (2024). The discontinuous Galerkin method for river-delta continuum by means of a coupled 1D-2D shallow water model. In Collectif (ed.), River Flow 2022 (p. p. 137-145). Taylor & Francis, CRC Press. https://doi.org/10.1201/9781003323037-19