Divergence-free bases and multiresolution methods for reduced-order flow modeling

AIAA journal

Volumn 38, Issue 12, 2000, Pages 2219-2232

  Ko, Jeonghwan ^a   Kurdila, Andrew J ^b   Rediniotis, Othon K ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

^b UNIVERSITY OF FLORIDA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; COMPUTATIONAL FLUID DYNAMICS; CORRELATION METHODS; FEATURE EXTRACTION; IMAGE ANALYSIS; IMAGE COMPRESSION; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; SIGNAL FILTERING AND PREDICTION; VELOCITY MEASUREMENT; WAVELET TRANSFORMS;

DIVERGENCE FREE WAVELETS; MULTIRESOLUTION ANALYSIS; PARTICLE IMAGE VELOCIMETRY; REDUCED ORDER FLOW MODELING;

AERODYNAMICS;

EID: 0034499922     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/2.912     Document Type: Article

References (38)

1. Daubechies, I., "Orthonormal Bases of Compactly Supported Wavelets," Communications on Pure and Applied Mathematics, Vol. 41, No. 7, 1988, pp. 909-996.
2. Chui, C. K. (ed.), Wavelets: A Tutorial in Theory and Applications, Academic, San Diego, CA, 1992, pp. 541-700.
3. Mallat, S., "A Theory for Multiresolution Signal Decomposition: The Wavelet Representation," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 11, No. 7, 1989, pp. 674-693.
4. DeVore, R. A., Jawerth, B., and Lucier, B. J., "Image Compression Through Wavelet Transform Coding," IEEE Transactions on Information Theory, Special Issue on Wavelet Transforms and Multiresolution Signal Analysis, Vol. 38, No. 2, 1992, pp. 719-746.
5. Jaffard, S., and Laurencot, P., "Orthonormal Wavelets, Analysis of Operators, and Applications to Numerical Analysis," Wavelets: A Tutorial in Theory and Applications, edited by C. Chui, Academic, San Diego, CA, 1992, pp. 543-601.
6. Ko, J., Kurdila, A. J., Gilarranz, J. L., and Rediniotis, O. K., "Particle Image Velocimetry via Wavelet Analysis," AIAA Journal, Vol. 36, No. 8, 1998, pp. 1451-1459.
7. Farge, M., Schneider, K., and Kevlahan, N., "Non-Gaussianity and Coherent Vortex Simulation for Two-Dimensional Turbulence Using an Adaptive Orthogonal Wavelet Basis," Physics of Fluids, Vol. 11, No. 8, 1999, pp. 2187-2201.
8. Sritharan, S. S. (ed.), Optimal Control of Viscous Flows, Society for Industrial and Applied Mathematics, Philadelphia, 1998, pp. 1-198.
9. Joshi, S. S., Speyer, J. L., and Kim, J., "A Systems Theory Approach to the Feedback Stabilization of Infinitesimal and Finite-Amplitude Disturbances in Plane Poiseuille Flow," Journal of Fluid Mechanics, Vol. 332, Feb. 1997, pp. 157-184.
10. Cortellezi, L., and Speyer, J., "Advance in Boundary Layer Control: Robust Reduced-Order Transition Controller," Computational and Applied Mathematics Rept. 97-57, University of California, Los Angeles, 1997.
11. Breuer, K. S., Amonlirdviman, K., and Rathnasingham,"Adaptive Feed-Forward Control of Turbulent Boundary Layers," AIAA Paper 98-1025, Jan. 1998.
12. Loeve, M., "Functions Aleatoire de Second Ordre," Compte Rendus Acad. Sci. Paris, Vol. 220, 1945.
13. Karhunen, K., "Zur Spektral Theorie Stochasticher Prozesse," Ann. Acad. Sci. Fennicae, Ser. A1, Vol. 34, 1946.
14. Lumley, J. L., "The Structure of Inhomogeneous Turbulent Flows," Atmospheric Turbulence and Radio Wave Propagation, edited by A. M. Yaglom and V. I. Tatarsky, Nauka, Moscow, 1967, pp. 166-178.
15. Reichert, R. S., Hatay, F. F., Biringen, S., and Huser, A., "Proper Orthogonal Decomposition Applied to Turbulent Flow in a Square Duct," Physics of Fluids, Vol. 6, No. 9, 1994, pp. 3086-3092.
16. Ly, H. V., and Tran, H. T., "Proper Orthogonal Decomposition for Flow Calculations and Optimal Control in a Horizontal CVD Reactor," Center for Research in Scientific Computation, TR CRSC-TR-98-13, North Carolina State Univ., Raleigh, NC, March 1998.
17. Tang, K. Y., Graham, W. R., and Peraire, J., "Active Flow Control Using a Reduced Order Model and Optimum Control," Proceedings of the 27th AIAA Fluid Dynamics Conference, AIAA, Reston, VA, 1996.
18. Aubry, N., Holmes, P., Lumley, J. L., and Stone, E., "The Dynamics of Coherent Structures in the Wall Region of a Turbulent Boundary Layer," Journal of Fluid Mechanics, Vol. 192, 1988, pp. 115-173.
19. Ball, K. S., Sirovich, L., and Keefe, L. R., "Dynamical Eigenfunction Decomposition of Turbulent Channel Flow," International Journal for Numerical Methods in Fluids, Vol. 12, No. 6, 1991, pp. 585-604.
20. Berkooz, G., Holmes, P., and Lumley, J. L., "The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows," Annual Review of Fluid Mechanics, Vol. 25, 1993, pp. 539-575.
21. Gunzburger, M. D., Finite Element Methods for Viscous Incompressible Flows: A Guide to Theory, Practice, and Algorithms, Academic, Boston, 1989, pp. 108-114.
22. Ito, K., and Ravindran, S. S., "Reduced Basis Method for Flow Control," Center for Research in Scientific Computation, TR CRSC-TR96-25, North Carolina State Univ., Raleigh, NC, Aug. 1996.
23. Ito, K., and Ravindran, S. S., "A Reduced Basis Method for Control Problems Governed by PDEs," Center for Research in Scientific Computation, TR CRSC-TR97-1, North Carolina State Univ., Raleigh, NC, Jan. 1997.
24. Ito, K., and Ravindran, S. S., "A Reduced-Order Method for Simulation and Control of Fluid Flow," Journal of Computational Physics, Vol. 143, No. 5, 1998, pp. 403-425.
25. Cohen, A., Daubechies, I., and Feauveau, J.-C., "Biorthogonal Bases of Compactly Supported Wavelets," Communications on Pure and Applied Mathematics, Vol. 45, No. 5, 1992, pp. 485-560.
26. Daubechies, I., Ten Lectures on Wavelets, Society of Industrial and Applied Mathematics, Philadelphia, 1992, pp. 156-166.
27. Lemarie-Rieusset, P., "Ondelettes Vecteurs a Divergence Nulle," Comptes Rendus de l'Academie des Sciences Serie I. Mathematique, Vol. 313, No. 5, 1991, pp. 213-216.
28. Lemarie-Rieusset, P., "Wavelets, Splines and Divergence-Free Vector Functions," Approximation Theory, Spline Functions and Applications, edited by S. P. Singh, Kluwer Academic, Norwell, MA, 1992, pp. 381-390.
29. Lemarie-Rieusset, P., "Un Theoreme d'Inexistence Pour les Ondelettes Vecteurs a Divergence Nulle," Comptes Rendus de l'Academie des Sciences Serie I. Mathematique, Vol. 319, No. 8, 1994, pp. 811-813.
30. Urban, K., "On Divergence-Free Wavelets," Advances in Computational Mathematics, Vol. 4, No, 1, 1995, pp. 51-82.
31. Urban, K., "Using Divergence Free Wavelets for the Numerical Solution of the Stokes Problem," Algebraic Multilevel Iterations, edited by O. Axelsson and B. Polman, Nijmegen Univ., Nijmegen, The Netherlands, 1996, pp. 259-278.
32. Chui, C. K., An Introduction to Wavelets, Academic Press, San Diego, CA, 1992, pp. 81-117.
33. Amitay, M., Smith B. L., and Glezer, A., "Aerodynamic Flow Control Using Synthetic Jet Technology," AIAA Paper 98-0208, Jan. 1998.
34. Smith D., Amitay, M., Kibens, V., Parekh, D., and Glezer, A., "Modifications of Lifting Body Aerodynamics Using Synthetic Jet Actuators," AIAA Paper 98-0209, Jan. 1998.
35. Seifert, A., Bachat, T., Koss, D., Shepshelovich, M., and Wygnanski, I., "Oscillatory Blowing: A Tool to Delay Boundary-Layer Separation," AIAA Journal, Vol. 31, No. 11, 1993, pp. 2052-2060.
36. Seifert, A., and Pack, L. G., "Oscillatory Control of Separation at High Reynolds Numbers," AIAA Paper 98-0214, Jan. 1998.
37. Donovan, G. C., Geronimo, J. S., and Hardin, D. P., "Intertwining Multiresolution Analyses and the Construction of Piecewise-Polynomial Wavelets," SIAM Journal of Mathematical Analysis, Vol. 27, No. 6, 1996, pp. 1791-1815.
38. Rediniotis, O. K., Ko, J., Yue, X., and Kurdila, A. J., "Synthetic Jets, Their Reduced-Order Modeling, and Applications to Flow Control," AIAA Paper 99-1000, Jan. 1999.