Fictitious domain for stabilization of fluid-structure interaction

International audienceWe study the numerical approximation of the fluid structure interaction for stabilization of the fluid flow around an unstable stationary solution in a two dimensional domain, in the presence of boundary perturbations. We use a feedback control law recently proposed in [Airiau et al. (2017)] which is able to stabilize the nonlinear semi-discrete controlled system and based on the fluid only. Using Dirichlet boundary feedback, we deduce a boundary structure displacement. The fluid structure closed loop feedback is tested numerically using a fictitious domain finite element method based on extended Finite Element