Controllability Approach for a Fluid Structure Interaction Problem

Abstract

The present paper presents a new method to solve fluid structure interaction problem. Our computational method is based on controllability approach. Given a target structural displacement we will find a control steering the displacement of the structure u to . We need to define a payoff functional (J): where u solves the structure equation for the control and is a fixed value. Our aim is to find a control which minimizes the payoff criterion. And therefore we find u the beam displacement, v the velocity of the fluid and p the pressure of the fluid.

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I. Mbaye, "Controllability Approach for a Fluid Structure Interaction Problem," Applied Mathematics, Vol. 3 No. 3, 2012, pp. 213-216. doi: 10.4236/am.2012.33034.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] A. Osses and J. P. Puel, “Approximate Controllability for a Linear Model of Fluid Structure Interactiont,” ESAIM Control, Optimization and Calculus of Variation, Vol. 4, 2000, pp. 497-513. doi:10.1051/cocv:1999119
[2] M. A. Fernandez and M. Moubachir, “And Exact Block Newton Algorithm for Solving Fluid Structure Interaction Problem,” Comptes Rendus de l’Academie des Sciences de Paris, Ser. I, Vol. 336, 2003, pp. 681-686.
[3] M. A. Fernandez and M. Moubachir, “A Newton Method Using Exact Jacobians for Solving Fluid-Structure Coupling,” Computers and Structures, Vol. 83. No. 2-3, 2005. doi:10.1016/j.compstruc.2004.04.021
[4] A. Quateroni, M. Tuveri and A. Veneziani, “Computational Vascular Fluid Dynamics, Problem Models and Methods,” Computing and Visualization in Science, Vol. 2, No. 4, 2000, pp. 163-197. doi:10.1007/s007910050039
[5] A. Blouza, L. Dumas and I. Mbaye, “Multiobjective Optimization of a Stent in a Fluid-Structure Context,” Proceedings GECCO, Atlanta, 12-16 July 2008, pp. 20562060. doi:10.1145/1388969.1389021
[6] C. Grandmont, “Existence et Unicité de Solution d’un Problème de Couplage Fluide-Structure Bidimensionnel stationnaire,”Comptes Rendus de l’Academie des Sciences de Paris, Ser. I, 1998.
[7] C. Murea and C. Maday, “Existence of an Optimal Control for a Nonlinear Fluid Cable Interaction Problem”, Rapport de Recherche CEMRACS, C.I.R.M., Luminy, 1996.
[8] F. Hecht and O. Pironneau, “A Finite Element Software for PDE FreeFem++,” 2003. www.rocq.inria.fr/Frederic.Hecht
[9] I. Mbaye and C. Murea, “Numerical Procedure with Analytic Derivative for Unsteady Fluid-Structure Interaction,” Communications in Numerical Methods in Engineering, Vol. 24, No. 11, 2008, pp. 1257-1271. doi:10.1002/cnm.1031
[10] C. Murea, “The BFGS Algorithm for Nonlinear Least Squares Problem Arising from Blood Flow in Arteries,” Computers & Mathematics with Applications, Vol. 49, 2005, pp. 171-186. doi:10.1016/j.camwa.2004.11.002

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