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Mathematical and numerical analysis

Models derived within the team to deal with complex flows must be first analysed to ensure existence and uniqueness of solutions and to determine their smoothness and their time interval of existence. If the theory of hyperbolic conservation laws is extensively addressed in the literature, multilayer or dispersive models exhibit a more complex structure. Hence team members are interested in the mathematical analysis of these models.

Likewise, numerical tools designed for the shallow water equations cannot directly apply to aforementioned models. Although simpler than the free surface Navier-Stokes equations, those layer-averaged models include difficult differential operators that require the construction of new numerical schemes. These schemes are expected to be robust as well as efficient in terms of computational costs in the purpose of implementing them into industrial codes.

This research theme is very competitive and numerous laboratories, in France and abroad, work on these research fields, among which: Italy, The Netherlands, USA, Germany and Spain. Our characteristic is to combine theoretical analysis and finalised results favouring dissemination and transfer.

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