Méthodes Level-Set et pénalisation pour le calcul d'interactions fluide-structure

Claire Bost 1
1 EDP - Equations aux Dérivées Partielles
LJK - Laboratoire Jean Kuntzmann
Abstract : This dissertation is dedicated to the study of fluid structure interaction problems with either the immersed boundary method or penalization.
The first part describes the numerical methods dedicated to the simulation of fluid-structure interaction models (flow formulation, structure localization, interactions treatment), then details the models we are dealing with in particular: incompressible fluid/elastic membrane and incompressible fluid/rigid solid.
In the second part we study the numerical stability of a level-set formulation of the immersed boundary method applied to fluid-elastic membrane coupling. A new stability condition for this model is derived by the linear analysis of a 1D model, and then validated numerically on a membrane relaxation test case.
Finally, in the third part we focus on the numerical analysis of a penalization method for fluid/solid coupling, in which the rigid velocity is computed by a projection method. We prove the convergence of the penalized problem toward a weak formulation. Then we propose some numerical evidence of the good behavior of our numerical method on a sedimentation test case.
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Theses
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https://tel.archives-ouvertes.fr/tel-00341209
Contributor : Claire Bost <>
Submitted on : Monday, November 24, 2008 - 4:43:48 PM
Last modification on : Friday, July 12, 2019 - 1:22:24 AM
Long-term archiving on: Monday, June 7, 2010 - 9:55:31 PM

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Claire Bost. Méthodes Level-Set et pénalisation pour le calcul d'interactions fluide-structure. Modélisation et simulation. Université Joseph-Fourier - Grenoble I, 2008. Français. ⟨tel-00341209⟩

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