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Developing mathematical theories of the physical world: Open Access research on fluid dynamics from Strathclyde

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On a 2D 'zoom' for the 1D shallow water model: coupling and data assimilation

Gejadze, I.Y. and Monnier, J. (2007) On a 2D 'zoom' for the 1D shallow water model: coupling and data assimilation. Computer Methods in Applied Mechanics end Engineering, 196 (45-48). pp. 4628-4643. ISSN 0045-7825

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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.