Adjoint optimal control problems for fluid-structure interaction systems

In the last years adjoint optimal control has been increasingly used for design and simulations in several research fields. Applications to Computational Fluid Dynamics problems dedicated to the study of transient-diffusion equations, shape optimization problems, fluid-solid conjugate heat transfer and turbulent flows can be found in literature. The study of Fluid-Structure Interaction problems gained popularity recently because of many interesting applications in engineering and biomedical fields. In this paper we study adjoint optimal control problems for Fluid-Structure Interaction systems in order to improve the advantages of using FSI simulations when designing engineering devices where fluid-dynamical interactions between a fluid and a solid play a significant role. We assess distributed optimal control problems with the purpose to control the fluid behavior by moving the solid region to obtain a desired fluid velocity in specific parts of the domain. The adjoint equations of the FSI monolithic system are derived and the optimality system solved for some simple cases with an in-house finite element code with mesh-moving capabilities for the study of large displacements in the solid. The approach presented in this work is general and can be used to assess different objectives and types of control in future works.