scholarly journals On the Optimal Control of Stationary Fluid–Structure Interaction Systems

Fluids ◽  
2020 ◽  
Vol 5 (3) ◽  
pp. 144
Author(s):  
Leonardo Chirco ◽  
Sandro Manservisi
Keyword(s):  
Optimal Control ◽  
Fluid Structure Interaction ◽  
Optimal Solution ◽  
Adjoint System ◽  
Optimality System ◽  
Necessary Condition ◽  
Optimal Controls ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Gradient Based

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.

scholarly journals Optimal Pressure Boundary Control of Steady Multiscale Fluid-Structure Interaction Shell Model Derived from Koiter Equations

Fluids ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 149
Author(s):  
Andrea Chierici ◽  
Leonardo Chirco ◽  
Sandro Manservisi
Keyword(s):  
Optimal Control ◽  
Solid Wall ◽  
Fluid Structure Interaction ◽  
Computational Cost ◽  
Robin Boundary Condition ◽  
Design Parameters ◽  
Fluid Structure ◽  
Control Approach ◽  
Structure Interaction ◽  
Fluid Boundary

Fluid-structure interaction (FSI) problems are of great interest, due to their applicability in science and engineering. However, the coupling between large fluid domains and small moving solid walls presents numerous numerical difficulties and, in some configurations, where the thickness of the solid wall can be neglected, one can consider membrane models, which are derived from the Koiter shell equations with a reduction of the computational cost of the algorithm. With this assumption, the FSI simulation is reduced to the fluid equations on a moving mesh together with a Robin boundary condition that is imposed on the moving solid surface. In this manuscript, we are interested in the study of inverse FSI problems that aim to achieve an objective by changing some design parameters, such as forces, boundary conditions, or geometrical domain shapes. We study the inverse FSI membrane model by using an optimal control approach that is based on Lagrange multipliers and adjoint variables. In particular, we propose a pressure boundary optimal control with the purpose to control the solid deformation by changing the pressure on a fluid boundary. We report the results of some numerical tests for two-dimensional domains to demonstrate the feasibility and robustness of our method.

scholarly journals Distributed optimal control applied to Fluid Structure Interaction problems

2019 ◽  
Vol 1224 ◽  
pp. 012003
Author(s):  
A Chierici ◽  
L Chirco ◽  
R Da Vià ◽  
M Manservisi ◽  
S Magnaniand
Keyword(s):  
Optimal Control ◽  
Fluid Structure Interaction ◽  
Distributed Optimal Control ◽  
Fluid Structure ◽  
Structure Interaction

scholarly journals An optimal control method for time-dependent fluid-structure interaction problems

2021 ◽  
Author(s):  
Yongxing Wang ◽  
Peter K. Jimack ◽  
Mark A. Walkley ◽  
Dongmin Yang ◽  
Harvey M. Thompson
Keyword(s):  
Control Method ◽  
Fluid Structure Interaction ◽  
Adjoint System ◽  
Descent Method ◽  
Interface Condition ◽  
Gradient Descent Method ◽  
Arbitrary Lagrangian Eulerian ◽  
Problem Size ◽  
Fluid Structure ◽  
Structure Interaction

AbstractIn this article, we derive an adjoint fluid-structure interaction (FSI) system in an arbitrary Lagrangian-Eulerian (ALE) framework, based upon a one-field finite element method. A key feature of this approach is that the interface condition is automatically satisfied and the problem size is reduced since we only solve for one velocity field for both the primary and adjoint system. A velocity (and/or displacement)-matching optimisation problem is considered by controlling a distributed force. The optimisation problem is solved using a gradient descent method, and a stabilised Barzilai-Borwein method is adopted to accelerate the convergence, which does not need additional evaluations of the objective functional. The proposed control method is validated and assessed against a series of static and dynamic benchmark FSI problems, before being applied successfully to solve a highly challenging FSI control problem.

Analysis and finite element discretization for optimal control of a linear fluid–structure interaction problem with delay

2018 ◽  
Vol 40 (1) ◽  
pp. 140-206
Author(s):  
Gilbert Peralta ◽  
Karl Kunisch
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Fluid Structure Interaction ◽  
Interaction Model ◽  
Necessary Optimality Conditions ◽  
Finite Element Discretization ◽  
Element Discretization ◽  
Fluid Structure ◽  
Delay Term ◽  
Structure Interaction

Abstract An optimal control problem for a linearized fluid–structure interaction model with a delay term in the structural damping is analyzed. A distributed control acting on the fluid domain, structure domain or both is considered. The necessary optimality conditions are derived both for rough and smooth initial data. A parabolic regularization of the problem and its convergence are investigated. Finite element discretization for the regularized problem and error estimates are provided. Piecewise linear elements with bubble functions for the fluid and a discontinuous Galerkin scheme for the spatial and temporal discretizations are utilized respectively. Numerical experiments illustrating the theoretical results are given.

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