Leonardo Chirco (d'Alembert) - Steady optimal control of fluid structure interaction systems

Fluid-structure interaction (FSI) systems consist of one or more solid structures that deform by interacting with a surrounding fluid flow and are commonly studied in many engineering and biomedical fields. These problems are characterized by an intrinsic mathematical challenge, due to the inherent nonlinearity given by a domain that moves as a function of the unknowns. Moreover, it is also interesting to study the inverse problem, where the goal is to find the optimal law of some control parameters, such that an objective functional is minimized. First, I will present the FSI monolithic system and a multiscale model, derived from the Koiter shell equations and used to reduce the dimensionality of the solid. Then, I will focus on the FSI steady optimization problem. I will introduce the adjoint and Lagrange multiplier formalisms used to derive the optimality system and finally, I will show and discuss some results obtained with distributed control and pressure boundary control.