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

G Delay , S Ervedoza (1) , Michel Fournié (1) , G Haine

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We 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.

Mots clés: fluid-structure interaction; DNS; fictitious domain; XFEM; control; incompressible flow

Domaines: Analyse numérique [math.NA]

G Delay, S Ervedoza, Michel Fournié, G Haine. 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. IUTAM Symposium on Critical flow dynamics involving moving/deformable structures with design applications, 2018, Santorini, Greece. ⟨hal-01978117⟩