Jacques Sainte-Marie is head of the research team ANGE and scientific head of the research group EGRIN-CNRS. ANGE is a joint research team between Inria, Univ. Paris 6, CNRS and CEREMA. The team aims at developing models, numerical methods and simulation tools for the approximation of free surface flows. The applications concern natural hazards, ecology, marine energy production,…
Free Surface Flows: from Hydrostatic to Non-Hydrostatic Models
The equations governing free surface flows, typically the Navier-Stokes equations, are difficult to analyse and solve and therefore reduced complexity models are often used to represent geophysical flows. During this presentation, we first present models able to approximate the hydrostatic Navier-Stokes equations. The associated numerical schemes are endowed with stability properties such as positivity, well-balancing and discrete entropy inequality. They are confronted with analytical solutions and experimental measurements. Then we propose non-hydrostatic (dispersive) models and numerical procedures to approximate them. But the numerical analysis of such models is complex and several questions remain opened.