NUMERICAL SIMULATION ON A FIXED MESH FOR THE FEEDBACK STABILIZATION OF A FLUID-STRUCTURE INTERACTION SYSTEM WITH A STRUCTURE GIVEN BY A FINITE NUMBER OF PARAMETERS

Abstract

International audienceWe study the numerical approximation of a 2d fluid-structure interaction problem stabilizing the fluid flow around an unstable stationary solution in presence of boundary perturbations. The structure is governed by a finite number of parameters and a feedback control law acts on their accelerations. The existence of strong solutions and the stabilization of this fluid-structure system were recently studied in [3]. The present work is dedicated to the numerical simulation of the problem using a fictitious domain method based on extended Finite Element [4]. The originality of the present work is to propose efficient numerical tools that can be extended in a simple manner to any fluid-structure control simulation. Numerical tests are given and the stabilization at an exponential decay rate is observed for small enough initial perturbations