Continuous mode interpolation for control-oriented models of fluid flow

Notes on Numerical Fluid Mechanics and Multidisciplinary Design

Volumn 95, Issue , 2007, Pages 260-278

  Morzyński, Marek ^a,b   Stankiewicz, Witold ^b   Noack, Bernd R ^a   King, Rudibert ^a   Thiele, Frank ^a   Tadmor, Gilead ^c  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b POZNAN UNIVERSITY OF TECHNOLOGY   (Poland)

^c Northeastern University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34548335257     PISSN: 16122909     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-71439-2_16     Document Type: Conference Paper

References (39)

1. Gad-el-Hak, M.: Flow Control: Passive, Active and Reactive Flow Management. Cambridge University Press (2000)
2. Fiedler, H. & Fernholz, H.H.: On the management and control of turbulent shear flows. Progr. Aeronaut. Sci. 27 (1990) 305-387
3. Becker, R., Garwon, M., Gutknecht, C., Bärwolff, G., King, R.: Regelung aerodynamischer Strömungen am Beispiel einer rückwärtsgewandten Stufe (transl.: Control of aerodynamics flows examplified for the backward-facing step). Automatisierungstechnik 50 (2002) 79-86
4. Gerhard, J., Pastoor, M., King, R., Noack, B.R., Dillmann, A., Morzyński, M., Tadmor, G.: Model-based control of vortex shedding using low-dimensional Galerkin models. AIAA-Paper 2003-4262, 33rd AIAA Fluids Conference and Exhibit, Orlando, Florida, USA (2003)
5. Rowley, C., Juttijudata, V.: Control and estimation of oscillating cavity flows. In 57th Annual Meeting of the Division of Fluid Dynamics of the American Physical Society. (2004) (Bulletin Am. Phys. Soc., Vol. 49, No. 9, AG.005)
6. Acton, F.: Numerical Methods that Work. Harper & Row, Publishers, New York, Evanston and London (1970)
7. Noack, B.R., Afanasiev, K., Morzyński, M., Tadmor, G., Thiele, F.: A hierarchy of low-dimensional models for the transient and post-transient cylinder wake. J. Fluid Mech. 497 (2003) 335-363
8. Luchtenburg, D., Tadmor, G., Lehmann, O., Noack, B.R., King, R., Morzyński, M.: Tuned POD Galerkin models for transient feedback regulation of the cylinder wake. AIAA-Paper 2006-1407, 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, USA (2006)
9. Stuart, J.: On the non-linear mechanics of hydrodynamic stability. J. Fluid Mech. 4 (1958) 1-21
10. Stuart, J.: Nonlinear stability theory. Ann. Rev. Fluid Mech. 3 (1971) 347-370
11. Holmes, P., Lumley, J., Berkooz, G.: Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press, Cambridge (1998)
12. Ladyzhenskaya, O.: The Mathematical Theory of Viscous Incompressible Flow. Gordon and Breach, New York, London (1963)
13. Fletcher, C.: Computational Galerkin Methods. Springer, New York (1984)
14. Siegel, S., Cohen, K., Seigel, J.,McLaughlin, T.: Proper orthogonal decomposition snapshot selection for state estimation of feedback controlled flows. AIAA-Paper 2006-1400, AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, USA (2006)
15. Noack, B.R., Eckelmann, H.: A low-dimensional Galerkin method for the three-dimensional flow around a circular cylinder. Phys. Fluids 6 (1994) 124-143
16. Noack, B.R., Eckelmann, H.: A global stability analysis of the steady and periodic cylinder wake. J. Fluid Mech. 270 (1994) 297-330
17. Noack, B.R., Papas, P., Monkewitz, P.: The need for a pressure-term representation in empirical Galerkin models of incompressible shear flows. J. Fluid Mech. 523 (2005) 339-365
18. King, R., Seibold, M., Lehmann, O., Noack, B.R., Morzy'nski, M., Tadmor, G.: Nonlinear flow control based on a low dimensional model of fluid flow. In Meurer, T., Graichen, K., Gilles, E., eds.: Control and Observer Design for Nonlinear Finite and Infinite Dimensional Systems, LNCIS 322. Springer (2005) 369-386
19. Noack, B.R., Tadmor, G., Morzyński, M.: Low-dimensional models for feedback flow control. Part I: Empirical Galerkin models. AIAA-Paper 2004-2408 (invited contribution), 2nd AIAA Flow Control Conference, Portland, Oregon,USA (2004)
20. Tadmor, G., Noack, B.R., Morzyński, M., Siegel, S.: Low-dimensional models for feedback flow control. Part II: Controller design and dynamic estimation. AIAA-Paper 2004-2409 (invited contribution), 2nd AIAA Flow Control Conference, Portland, Oregon, USA (2004)
21. Busse, F.: Numerical analysis of secondary and tertiary states of fluid flow and their stability properties. Appl. Sci. Res. 48 (1991) 341-351
22. Boberg, L., Brosa, U.: Onset of turbulence in a pipe. Z. Naturforsch. 43a (1988) 697-726
23. Rummler, B.: Zur Lösung der instationären inkompressiblen Navier-Stokesschen Gleichungen in speziellen Gebieten (transl.: On the solution of the incompressible Navier-Stokes equations in some domains). Habilitationsschrift, Fakultät für Mathematik, Ottovon-Guericke-Universität Magdeburg (2000)
24. Bewley, T., Liu, S.: Optimal and robust control and estimation of linear paths to transition. J. Fluid Mech. 365 (1998) 305-349
25. Dušek, J., Le Gal, P., Fraunie, P.: A numerical and theoretical study of the first Hopf bifurcation in a cylinder wake. J. Fluid Mech. 264 (1994) 59-80
26. Zielinska, B., Wesfreid, J.: On the spatial structure of global modes in wake flow. Phys. Fluids 7 (1995) 1418-1424
27. Noack, B.R., Tadmor, G., Morzyński, M.: Actuation models and dissipative control in empirical Galerkin models of fluid flows. In The 2004 American Control Conference, Boston, MA, USA (2004) Paper FrP15.6 0001-0006
28. Rediniotis, O., Ko, J., Kurdila, A.: Reduced order nonlinear Navier-Stokes models for synthetic jets. J. Fluids Enrng. 124 (2002) 433-443
29. Deane, A., Kevrekidis, I., Karniadakis, G., Orszag, S.: Low-dimensional models for complex geometry flows: Application to grooved channels and circular cylinders. Phys. Fluids A 3 (1991) 2337-2354
30. Khibnik, A., Narayanan, S., Jacobson, C., Lust, K.: Analysis of low dimensional dynamics of flow separation. In Continuation Methods in Fluid Dynamics. Notes on Numerical Fluid Mechanics, vol. 74, Vieweg (2000) 167-178 Proceedings of ERCOFTAC and Euromech Colloquium 383, Aussois, France (1998)
31. Ma, X., Karniadakis, G.: A low-dimensional model for simulating three-dimensional cylinder flow. J. Fluid Mech. 458 (2002) 181-190
32. Jørgensen, B., Sørensen, J., Brøns, M.: Low-dimensional modeling of a driven cavity flow with two free parameters. Theoret. Comput. Fluid Dynamics 16 (2003) 299-317
33. Bergmann, M., Cordier, L., Brancher, J.P.: Optimal rotary control of the cylinder wake using proper orthogonal decomposition reduced order model. Phys. Fluids 17 (2005) 097101-097121
34. Morzyński, M., Afanasiev, K., Thiele, F.: Solution of the eigenvalue problems resulting from global non-parallel flow stability analysis. Comput. Meth. Appl. Mech. Enrgrg. 169 (1999) 161-176
35. Zebib, A.: Stability of viscous flow past a circular cylinder. J. Engr. Math. 21 (1987) 155-165
36. Unal, M., Rockwell, D.: On the vortex formation from a cylinder; Part2. Control by a splitter-plate interference. J. Fluid Mech. 190 (1987) 513-529
37. Mittal, S.: Effect of a "slip" splitter plate on vortex shedding from a cylinder. Phys. Fluids 9 (2003) 817-820
38. Strykowski, P., Sreenivasan, K.: On the formation and suppression of vortex 'shedding' at low Reynolds numbers. J. Fluid Mech. 218 (1990) 71-107
39. Lehmann, O., Luchtenburg, M., Noack, B.R., King, R., Morzyński, M., Tadmor, G.: Wake stabilization using POD Galerkin models with interpolated modes. In 44th IEEE Conference on Decision and Control and European Control Conference ECC 2005, Seville, Spain (2005) Invited Paper 1608