15/05/2014 - 11:00 Mr Daniel Le Roux (Université Claude Bernard Lyon 1) Salle 1 - Tour IRMA
The shallow-water system, obtained from the Navier-Stokes equations by vertical averaging, is extensively used in environmental studies (ocean, atmosphere, rivers) to simulate the propagation of typical waves (inertia-gravity, Rossby, ...). For most of the discretization schemes, the numerical approximation of shallow-water models leads to the appearance of spurious (non physical) solutions in the representation of the waves. In order to understand these difficulties and to select appropriate spatial discretization schemes, discrete analyses may be performed. The aim of this talk is to present such results in the context of continuous and mostly discontinuous Galerkin methods, and to propose a class of possible discretization schemes that is not affected by the spurious modes. Both discrete analyses and numerical simulations involving wave propagation for environmental problems will be presented.