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Fluid–structure interaction (FSI) systems consist of a fluid which flows and deforms one or more solid surrounding structures. In this paper, we study inverse FSI problems, where the goal is to find the optimal value of some control parameters, such that the FSI solution is close to a desired one. Optimal control problems are formulated with Lagrange multipliers and adjoint variables formalism. In order to recover the symmetry of the stationary state-adjoint system an auxiliary displacement field is introduced and used to extend the velocity field from the fluid into the structure domain. As a consequence, the adjoint interface forces are balanced automatically. We present three different FSI optimal controls: inverse parameter estimation, boundary control and distributed control. The optimality system is derived from the first order necessary condition by taking the Fréchet derivatives of the augmented Lagrangian with respect to all the variables involved. The optimal solution is obtained through a gradient-based algorithm applied to the optimality system. In order to support the proposed approach and compare these three optimal control approaches numerical tests are performed.

This paper deals with boundary optimal control problems for the Navier-Stokes equations and Wilcox turbulence model. In this paper we study adjoint optimal control problems for Navier-Stokes equations to improve the advantages of using simulations where turbulence models play a significant role in designing engineering devices. We assess first distributed optimal control problems with the purpose to control the fluid behavior by injecting a flow on the boundary solid region to obtain a desired control over the fluid velocity and the kinetic turbulence energy in specific parts of the domain. Then, with the same purpose, we use lifting functions and boundary control. For this reason we reformulate the boundary optimal control problem into a distributed problem through a lifting function approach. The stronger regularity requirements which are imposed by standard boundary control approaches can then be avoided. The state, adjoint and control equations are derived and the optimality system solved for some simple cases with a finite element. Furthermore, we propose numerical strategies that allow to solve the coupled optimality system in a robust way for a large number of unknowns. The approach presented in this work is general and can be used to assess different objectives and types of control.

Nowadays, many open-source numerical codes are available to solve physical problems in structural mechanics, fluid flow, heat transfer, and neutron diffusion. However, even if these codes are often highly specialized in the numerical simulation of a particular type of physics, none of them allows simulating complex systems involving all the physical problems mentioned above. In this work we present a numerical framework, based on the SALOME platform, developed to perform multiscale and multiphysics simulations involving all the mentioned physical problems. In particular, the developed numerical platform includes the multigrid finite element in-house code FEMuS for heat transfer, fluid flow, turbulence and fluid-structure modeling; the open-source finite volume CFD software OpenFOAM; the multiscale neutronic code DONJON-DRAGON; and a system-scale code used for thermal-hydraulic simulations. Efficient data exchange among these codes is performed within computer memory by using the MED libraries, provided by the SALOME platform.

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