Simulation des écoulements à la surface libre dans des environnements côtiers et estuariens : développement numérique et application sur des maillages non-structurés

Abstract

Over the last decades, there has been considerable attention in the accurate mathematical modeling and numerical simulations of free surface wave propagation in near-shore environments. A physical correct description of the large scale phenomena, which take place in the shallow water region, must account for strong nonlinear and dispersive effects, along with the interaction with complex topographies. First, a study on the behavior in nonlinear regime of different Boussinesq-type models is proposed, showing the advantage of using fully-nonlinear models with respect to weakly-nonlinear and weakly dispersive models (commonly employed). Secondly, a new flexible strategy for solving the fully-nonlinear and weakly-dispersive Green-Naghdi equations is presented, which allows to enhance an existing shallow water code by simply adding an algebraic term to the momentum balance and is particularly adapted for the use of hybrid techniques for wave breaking. Moreover, the first discretization of the Green-Naghdi equations on unstructured meshes is proposed via hybrid finite volume/ finite element schemes. Finally, the models and the methods developed in the thesis are deployed to study the physical problem of bore formation in convergent alluvial estuary, providing the first characterization of natural estuaries in terms of bore inception.