Models and numerical schemes for free surface flows. Beyond the Saint-Venant system

Abstract : This document is an overview of the research activities carried out by the author in geophysical flows modeling and in biomechanics. Because of the scales~-- in space and time~-- of the considered problems in geophysics, there exists a demand for models of reduced complexity such as Shallow Water type models but able to represent complex flows (dam breaks, floodings, avalanches,...). We propose several models approximating the free surface Navier-Stokes equations and extending the classical Saint-Venant system. For each of them, the derivation and a numerical scheme are given. The discrete model is then confronted with with analytical solutions and/or exprimental data associated with complex flows. The numerical schemes we propose rely on a kinetic interpretation of each of the models, the microscopic description allowing to prove necessary stability conditions of the schemes. Several of the proposed models have been implemented in industrial codes. Other contributions dealing with modeling in biomechanics and especially the electro-mechanical activity of the heart are also presented.
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Submitted on : Monday, January 3, 2011 - 7:48:15 PM
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Jacques Sainte-Marie. Models and numerical schemes for free surface flows. Beyond the Saint-Venant system. Mathematics [math]. Université Pierre et Marie Curie - Paris VI, 2010. ⟨tel-00551488⟩

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