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On a 2D ‘zoom’ for the 1D shallow water model: coupling and data assimilation. (English) Zbl 1173.76309
Summary: In the context of river hydraulics we elaborate the idea of a ‘zoom’ model locally superposed on an open-channel network global model. The zoom model (2D shallow water equations) describes additional physical phenomena, which are not represented by the global model (1D shallow water equations with storage areas). Both models are coupled using the optimal control approach when the zoom model is used to assimilate local observations into the global model (variational data assimilation) by playing the part of a mapping operator. The global model benefits from using zooms, while no substantial modification to it is required. Numerical results on a toy test case show the feasibility of the suggested method.

MSC:
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76M30 Variational methods applied to problems in fluid mechanics
76M12 Finite volume methods applied to problems in fluid mechanics
Software:
TAPENADE
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