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Analyse d'un problème d'interaction fluide-structure avec des conditions aux limites de type frottement à l'interface

Abstract : This PHD thesis is devoted to the theoretical and numerical analysis of a stationary fluid-structure interaction problem between an incompressible viscous Newtonian fluid, modeled by the 2D Stokes equations, and a deformable structure modeled by the 1D beam equations.The fluid and structure are coupled via a friction boundary condition at the fluid-structure interface.In the theoretical study, we prove the existence of a unique weak solution, under small displacements, of the fluid-structure interaction problem under a slip boundary condition of friction type (SBCF) by using Schauder fixed point theorem.In the numerical analysis, we first study a mixed finite element approximation of the Stokes equations under SBCF.We also prove an optimal a priori error estimate for regular data and we provide numerical examples.Finally, we present a fixed point algorithm for numerical simulation of the coupled problem under nonlinear boundary conditions.
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  • HAL Id : tel-02132280, version 1

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Hela Ayed. Analyse d'un problème d'interaction fluide-structure avec des conditions aux limites de type frottement à l'interface. Physique mathématique [math-ph]. Normandie Université; École nationale d'ingénieurs de Tunis (Tunisie), 2017. Français. ⟨NNT : 2017NORMC213⟩. ⟨tel-02132280⟩

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