Une approche eulérienne du couplage fluide-structure, analyse mathématique et applications en biomécanique

Thomas Milcent 1
1 EDP - Equations aux Dérivées Partielles
LJK - Laboratoire Jean Kuntzmann
Abstract : The interaction of an elastic structure and an incompressible fluid occurs in many phenomena in physics. This is the case in biomechanics where an elastic vesicle is immersed in a fluid. In this context, we consider a eulerian formulation of the immersed boundary method. A level set function is used to capture the interface and take into account the elasticity of the membrane. The first part is devoted to a theorem of local existence in time for this model. The demonstration is based on apriori non hilbertian estimates. We add to the model an bending energy depending on the curvature which allows in particular to obtain the equilibrium shapes of vesicles. In the second part we compare different methods of shape optimization to compute the force associated with this energy. We prove that these approaches lead to identical results. In application, we present in the latter part numerical simulations of equilibrium shapes and shear of vesicles.
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Thomas Milcent. Une approche eulérienne du couplage fluide-structure, analyse mathématique et applications en biomécanique. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2009. Français. ⟨tel-00399435⟩

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