Interval-based reduced-order models for unsteady fluid flow

International Journal of Numerical Analysis and Modeling

Volumn 4, Issue 3-4, 2007, Pages 353-367

  Borggaard, Jeff ^a   Hay, Alexander ^b   Pelletier, Dominique ^b  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

^b ÉCOLE POLYTECHNIQUE DE MONTRÉAL   (Canada)

Author keywords

Optimization; Principal interval decomposition; Proper orthogonal decomposition; Reduced order modeling; Surrogate model

Indexed keywords

EID: 50049084305     PISSN: 17055105     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (33)

1. A.C. Antoulas. Approximation of Large-Scale Dynamical Systems. Advances in Design and Control. SIAM, Philadelphia, 2005.
2. J. Borggaard. Optimal reduced-order modeling for nonlinear distributed parameter systems. In 2006 American Control Conference, 2006. Paper WeB13.3.
3. J. Borggaard, J. Burns, E. Cliff, and M. Gunzburger. Sensitivity calculations for a 2D, inviscid, supersonic forebody problem. In H. T. Banks, R. Fabiano, and K. Ito, editors, Identification and Control of Systems Governed by Partial Differential Equations, pages 14-24, Philadelphia, PA, 1993. SIAM Publications.
4. M. Breuer, J. Bernsdorf, T. Zeiser, and F. Durstf. Accurate computation of the laminar flow past a square cylinder based on two different methods: Lattice-Boltzmann and finite volume. International Journal of Heat and Fluid Flow, 21:186-196, 2000.
5. J. Burkardt, Q. Du, M. Gunzburger, and H.-C. Lee. Reduced order modeling of complex systems. In Proc. 20th Biennial Conference on Numerical Analysis, pages 29-38, 2003.
6. M. Couplet, C. Basdevant, and P. Sagaut. Calibrated reduced-order POD-Galerkin system for fluid flow modeling. Journal of Computational Physics, 207(1):192-220, 2005.
7. R.W. Davis, E.F. Moore, and L.P. Purtell. A numerical-experimental study on confined flow around rectangular cylinders. Physics of Fluids, 23:46-59, 1984.
8. M.Ö. Efe and H. Özbay. Low dimensional modelling and Dirichlét boundary controller design for Burgers equation. International Journal of Control, 44(10):895-906, 2004.
9. B. Galletti, C.H. Bruneau, L. Zannetti, and A. Iollo. Low-order modelling of laminar flow regimes past a confined square cylinder. Journal of Fluid Mechanics, 503:161-170, 2004.
10. S. Ganapathysubramanian and N. Zabaras. Design across length scales: A reduced-order model of polycrystal plasticity for the control of microstructure-sensitive material properties. Computation Methods in Applied Mechanics and Engineering, 193:5017-5034, 2004.
11. M. Gunzburger. Finite Element Methods for Viscous Incompressible Flows: A Guide to Theory, Practice and Algorithms. Academic Press, 1989.
12. M. Gunzburger. Perspectives in Flow Control and Optimization. SIAM, 2002.
13. P. Holmes, J.L. Lumley, and G. Berkooz. Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press, 1996.
14. H. Hotelling. Analysis of a complex of statistical variables with principal components. Journal of Educational Psychology, 24:417-441, 1933.
15. H. Hristova. Analyse de sensibility d'ecoulements instationnaires visqueux laminaires. Master's thesis, École Polytechnique de Montréal, 2003.
16. W.L. IJzerman. Signal representation and modeling of spatial structures in fluids. PhD thesis, Universiteit Twente, 2000.
17. K. Ito and S.S. Ravindran. A reduced-order method for simulation and control of fluid flows. Journal of Computational Physics, 143(2):403-425, 1998.
18. D.A. Jones, L.G. Margolin, and E.S. Titi. On the effectiveness of the approximate inertial manifold-a computational study. Theoretical and Computational Fluid Dynamics, 7:243-260, 1995.
19. K. Karhunen. Zur spektraltheorie stochastischer prozesse. Annales Academiae Scientarum Fennicae, 37, 1946.
20. D. Kovacs. Inertial manifolds and nonlinear Galerkin methods. Master's thesis, Virginia Tech, 2005.
21. K. Kunisch, S. Volkwein, and L. Xie. HJB-POD-based feedback design for the optimal control of evolution problems. SIAM Journal on Applied Dynamical Systems, 3(4):701-722, 2004.
22. M. Loève. Probability Theory. Van Nostrand, New York, 1955.
23. E.N. Lorenz. Empirical orthogonal functions and statistical weather prediction. Technical report, M.I.T., 1956.
24. M. Marion and R. Temam. Nonlinear Galerkin methods. SIAM Journal of Numerical Analysis, 26(5):1139-1157, 1989.
25. B. Noack, G. Tadmor, and M. Morzyński. A hierarchy of low-dimensional models for the transient and post-transient cylinder wake. J. Fluid Mechanics, 497:335-363, 2003.
26. B.R. Noack and H. Eckelmann. A low-dimensional Galerkin method for the three-dimensional flow around a circular cylinder. Physics of Fluids, 6:124-143, 1994.
27. A. Okajima. Strouhal number of rectangular cylinders. Journal of Fluid Mechanics, 123:379-398, 1982.
28. J.S. Peterson. The reduced basis method for incompressible viscous flow calculations. SIAM Journal on Scientific and Statistical Computing, 10(4):777-786, 1989.
29. C.W. Rowley and D.R. Williams. Dynamics and control of high-Reynolds-number flow over open cavities. Annual Review of Fluid Mechanics, 38:251-276, 2006.
30. A.K. Saha, G. Biswas, and K. Muralidhar. Three-dimensional study of flow past a square cylinder at low Reynolds numbers. International Journal of Heat and Fluid Flow, 24:54-66, 2003.
31. S. Sirisup and G.E. Karniadakis. A spectral viscosity method for correcting the long-term behavior of POD models. Journal of Computational Physics, 194:92-116, 2004.
32. K. Willcox, O. Ghattas, B. van Bloemen Waanders, and B. Bader. An optimization framework for goal-oriented, model-based reduction of large-scale systems. In Joint 44th IEEE CDC and ECC conference, Seville, Spain, 2005.
33. K. Willcox and A. Megretski. Fourier series for accurate, stable, reduced-order models in large-scale linear applications. SIAM Journal on Scientific Computing, 26(3):944-962, 2005.