Solving inverse problems involving the Navier-Stokes equations discretized by a Lagrange-Galerkin method

Computer Methods in Applied Mechanics and Engineering

Volumn 194, Issue 6-8, 2005, Pages 877-906

  Fourestey, Gilles ^a   Moubachir, Marwan ^b  

^a INRIA   (France)

^b Lab Central des Ponts et Chaussees   (France)

Author keywords

ALE formulation; Characteristics; Inverse problem; Lagrange Galerkin; Navier Stokes equations; Optimal boundary control of the tracking type; Quasi Newton methods

Indexed keywords

GALERKIN METHODS; INCOMPRESSIBLE FLOW; LAGRANGE MULTIPLIERS; NAVIER STOKES EQUATIONS; NEWTONIAN FLOW; PROBLEM SOLVING;

FAR-FIELD VELOCITY; LAGRANGE-GALERKIN SCHEME; LINEARIZED SCHEME; NONLINEAR ADVECTION OPERATORS;

INVERSE PROBLEMS;

BLUFF BODY; DRAG REDUCTION; INCOMPRESSIBLE FLUID; NAVIER-STOKES EQUATIONS; NEWTONIAN FLUID;

EID: 10644288677     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2004.07.006     Document Type: Article

References (32)

1. F. Abergel R. Temam On some control problems in fluid mechanics Theor. Comput. Fluid Dyn. 1 1990 303-325
2. A.K. Alekseev On estimation of entrance boundary parameters from downstream measurements using adjoint approach Int. J. Numer. Methods Fluids 36 8 2001 971-982
3. X. Amandolèse, Contribution à l'étude des chargements fluides sur des obstacles non profilés fixes ou mobiles: Application aux tabliers de pont. PhD thesis, Ecole Nationale des Ponts et Chaussées, 2001
4. Benqué J.-P., Ibler B., Keramsi A., Labadir G. A finite element method for the Navier-Stokes equations, in: Proceedings of the Third International Conference on Finite Elements in Flow Problems, 1980
5. M. Berggren Numerical solution of a flow-control problem: Vorticity reduction by dynamic boundary action SIAM J. Sci. Comput. 19 3 1998 829-860
6. F.J. Bonnans J.-C. Gilbert C. Lemaréchal C. Sagastizábal Numerical Optimization - Theoretical and Practice Aspects Mathématiques & Applications vol. xii 1997 Springer New York
7. R.H. Byrd P. Lu J. Nocedal C. Zhu A limited memory algorithm for bound constrained optimization SIAM J. Sci. Comput. 16 5 1995 1190-1208
8. M. Chevalier, Adjoint based Control and Optimization of Aerodynamic Flows. PhD thesis, Department of Mechanics, Royal Institute of Technology, 2002
9. M. Clerc, P. Le Tallec, M. Mallet, Optimal control for the parabolized Navier-Stokes system, Technical report, INRIA, RR-2653, 1995
10. J.-M. Coron On the controllability of the 2-D incompressible Navier-Stokes equations with the Navier slip boundary conditions ESAIM, Control Optim. Calc. Var. 1 1996 35-75
11. M.A. Fernández, Simplified Models in Fluid-Structure Interaction Problems, PhD thesis, University of Paris Dauphine, 2001
12. M.A. Fernández M. Moubachir Sensitivity analysis for an incompressible aeroelastic system Math. Models Methods Appl. Sci. 12 8 2002 1109-1130
13. E. Fernández-Cara On the approximate and null controllability of the Navier-Stokes equations SIAM Rev. 41 2 1999 269-277
14. G. Fourestey, Une méthode des caractéristiques d'ordre deux sur maillages mobiles pour la résolution des équations de Navier-Stokes, Technical report, INRIA, RR-4448, 2002
15. G. Fourestey, M. Moubachir, Optimal control of Navier-Stokes equations using Lagrange-Galerkin methods, Technical report, INRIA, RR-4609, 2002
16. A. Fursikov M. Gunzburger L. Hou Trace theorems for three-dimensional, time-dependent solenoidal vector fields and their applications Trans. Am. Math. Soc. 354 3 2002 1079-1116
17. A.V. Fursikov Optimal Control of Distributed Systems. Theory and Applications Translations of Mathematical Monographs 187 2000 American Mathematical Society Providence, RI
18. A.V. Fursikov M.D. Gunzburger L.S. Hou Boundary value problems and optimal boundary control for the Navier-Stokes system: The two-dimensional case SIAM J. Control Optim. 36 3 1998 852-894
19. V. Girault P.A. Raviart Finite Element Methods for Navier-Stokes Equations 1986 Springer-Verlag New York
20. M.D Gunzburger S. Manservisi The velocity tracking problem for Navier-Stokes flows with bounded distributed controls SIAM J. Control Optim. 37 6 1999 1913-1945
21. M.D. Gunzburger S. Manservisi The velocity tracking problem for Navier-Stokes flows with boundary control SIAM J. Control Optim. 39 2 2000 594-634
22. J.-W. He R. Glowinski R. Metcalfe A. Nordlander J. Periaux Active control and drag optimization for flow past a circular cylinder. I: oscillatory cylinder rotation J. Comput. Phys. 163 1 2000 83-117
23. M. Hinze K. Kunisch Second order methods for optimal control of time-dependent fluid flow SIAM J. Control Optim. 40 3 2001 925-946
24. C. Homescu I.M. Navon Z. Li Suppression of vortex shedding for flow around a circular cylinder using optimal control Int. J. Numer. Methods Fluids 38 1 2002 43-69
25. O.Y. Imanuvilov Remarks on exact controllability for the Navier-Stokes equations ESAIM, Control Optim. Calc. Var. 6 2001 39-72
26. D.C. Liu J. Nocedal On the limited memory BFGS method for large scale optimization Math. Program., Ser. B 45 3 1989 503-528
27. A. Maruoka M. Marin M. Kawahara Optimal control in Navier-Stokes equations Int. J. Comput. Fluid Dyn. 9 1998 313-322
28. G. Medic, B. Mohammadi, Optimal control of 3D turbulent flow over circular cylinder, in: 4th AIAA CFD Conference - Norfolk, VI, USA, AIAA Paper, AIAA-99-3654, 1999
29. B. Mohammadi O. Pironneau Applied Shape Optimization for Fluids Numerical Mathematics and Scientific Computation vol. xvi 2001 Clarendon Press Oxford 251
30. M. Moubachir, Control of fluid-structure interaction phenomena: application to the aeroelastic stability PhD thesis, Ecole Nationale des Ponts et Chaussées 2002
31. M. Moubachir, J.-P. Zolésio, Optimal control of fluid-structure interaction systems: The case of a rigid body Technical report, INRIA, RR-4611 2002
32. J. Nocedal, S.J. Wright, Numerical Optimization, in: Springer Series in Operations Research, 1999