Coupling superposed 1D and 2D shallow-water models: source terms and finite volume schemes

Enrique D. Fernandez-Nieto 1 Joel Marin 2 Jerome Monnier 2
2 MOISE - Modelling, Observations, Identification for Environmental Sciences
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : We study the superposition of 1D and 2D shallow-water equations with non-flat topographies, in the context of river-flood modeling. Since we superpose both models in the bi-dimensional areas, we focus on the definition of the coupling term required in the 1D equations. Using explicit finite volume schemes, we propose a definition of the discrete coupling term leading to schemes globally well-balanced (the glo- bal scheme preserves water at rest whatever if overflowing or not). For both equations (1D and 2D), we can consider independent finite volume schemes based on well-balanced Roe, HLL, Rusanov or other scheme, then the resulting global scheme remains well-balanced. We perform a few numerical tests showing on the one hand the well-balanced property of the resulting global numerical model, on the other hand the accuracy and robustness of our superposition approach. Therefore, the definition of the coupling term we present allows to superpose a local 2D model over a 1D main channel model, with non-flat topographies and mix incoming-outgoing lateral fluxes, using independent grids and finite vol- ume solvers.
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Enrique D. Fernandez-Nieto, Joel Marin, Jerome Monnier. Coupling superposed 1D and 2D shallow-water models: source terms and finite volume schemes. Computers and Fluids, Elsevier, 2010, 39 (6), pp.1070-1082. ⟨10.1016/j.compfluid.2010.01.016⟩. ⟨hal-00908275⟩

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