Abstract
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.
Highlights
Optimization has always been a key aspect in the field of engineering in order to improve the performance of an existing design or to improve its capability
If one has at hand a well tested Fluid–structure interaction (FSI) direct solver, the adjoint solver can be obtained with minor changes
In Algorithm 1 we reported a description of the steepest descent method used to solve the optimality system
Summary
Optimization has always been a key aspect in the field of engineering in order to improve the performance of an existing design or to improve its capability. When the problem becomes complex, the use of the appropriate optimization techniques is instead essential. We consider adjoint based methods since they have a solid mathematical background. This mathematical approach allow us to evaluate the well-posedness of the problem, the existence of local optimal solutions and the investigation of several numerical convergence issues. Adjoint solvers have commonly been implemented in commercial software, such as ANSYS, but the exact solution of an optimal problem remains a difficult task due to the definition of appropriate solution spaces and differentiability issues. When the solution space is well-defined and the control problem differentiable, the adjoint methods have been proven to be good tools for the optimal control of fluid dynamics complex problems, see, for example, [2,3]
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