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Habilitation à diriger des recherches

Modélisation, Analyse et Approximation numérique en mécanique des fluides

Abstract : This work is devoted to the derivation of models for complex fluids flows, to their theoretical analysis but also to the construction and analysis of adapted numerical methods.

In a first part, we are interested in diffuse interface models for multi-phase incompressible flows. We first propose various results concerning two-phase models, then we concentrate on the generalisation of the models to three-phase flows, which lead us to the important notion of consistency of the models. Numerical results confirm that the proposed models are physically relevant. Then, we consider the more classical non-homogeneous incompressible Navier-Stokes problem for which we propose a nonlinear open outflow boundary condition that we analyse. One of the tool developed to this end but interesting for itself, is the sharp study of trace properties for solutions to the transport equation with Sobolev regularity velocity field.

In a second part, we are interested in the finite volume numerical approximation of solutions to nonlinear monotonic elliptic problems (like the p-laplacian). We describe, in a first chapter, various results obtained for cartesian meshes. The second chapter is devoted to the study of more general geometric situations in the Discrete duality framework. We pay a particular attention to the case where the coefficients of the problem are allowed to be discontinuous, which leads to nonlinear transmission problems.

We conclude by describing some related workd, concerning a class of finite volume schems for linear elliptic problems on non-orthogonal meshes in the one hand, and a numerical study of coupled 2D/1D models coming from the asymptotic modeling of flows in fractured porous media, in the other hand.
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Habilitation à diriger des recherches
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https://tel.archives-ouvertes.fr/tel-00104532
Contributor : Franck Boyer <>
Submitted on : Friday, October 6, 2006 - 5:35:35 PM
Last modification on : Monday, January 14, 2019 - 10:02:04 AM
Long-term archiving on: : Tuesday, April 6, 2010 - 6:52:50 PM

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Franck Boyer. Modélisation, Analyse et Approximation numérique en mécanique des fluides. Mathématiques [math]. Université de Provence - Aix-Marseille I, 2006. ⟨tel-00104532⟩

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