A method for coupling 1D and 2D models used to simulate floods and its application to the Niger inner delta | Une méthode pour coupler des modèles 1D et 2D utilisés pour simuler des inondations et son application au delta intérieur du Niger

For calculating flood hazard, 2-D models are more and more used replacing 1-D models because they permit to obtain a detailed view of the flooding patterns. However, a 2-D calculation on large areas remains time consuming. Thus, one alternative consists in coupling 1-D and 2-D models. Often, the 1-D model is dedicated to the areas such as the river main channel in which the flow velocity direction can be fixed to a hydraulic axis all over the flood duration; conversely, the 2-D model is limited to the areas such as flood plains in which the flow pattern evolves with time. Another usual case for coupled model is the one of urban floods in which the drainage network is represented using a 1-D model and the overflow detailed using a 2-D model. The coupled model was built from the software Rubar 3 that solves 1-D de Saint Venant equations using an explicit second order Godunov type numerical scheme and the software Rubar 20 that solves 2-D shallow water equations using a similar explicit second order Godunov type numerical scheme. Both models permit the use of hydraulic structures equations locally if flow becomes complex. Because of these latter similarities, the exchange terms are the fluxes (of mass and of momentum) through the boundaries between the areas dedicated to each model. Thus, the calculation of these fluxes is performed at intermediate time taking into account the variables of both models. The remaining difficulty stands in defining a calculation method of these fluxes that can represent the physical processes at the boundary. The validation of the coupled model can be performed by comparison with 2-D model, which is easy and has the advantage to evaluate only the replacement of 2-D by 1-D and coupling; to go further, comparisons with experimental results remind the need to introduce a right (i.e. physically meaningful) representation of the coupling term. Another key point is the capacity of the model to adapt to very complex cases. One example is detailed in this paper: the annual flood in the inner Niger delta.