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

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 Delay (2018). The present work is dedicated to the numerical simulation of the problem using a fictitious domain method based on extended Finite Element Fournié and Lozinski (2018). 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.

To cite this paper:
Delay Guillaume, Ervedoza Sylvain, Fournié Michel, Haine Ghislain (2021) 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. In: Advances in Critical Flow Dynamics Involving Moving/Deformable Structures with Design Applications. Notes on Numerical Fluid Mechanics and Multidisciplinary Design; 147:195–211. Springer, Cham. Santorini, Greece.

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