Model reduction for large-scale CFD applications using the balanced proper orthogonal decomposition

17th AIAA Computational Fluid Dynamics Conference

Volumn , Issue , 2005, Pages

  Bui Thanh, T ^a   Willcox, K ^a  

^a Massachusetts Institute of Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AEROELASTICITY; CONTROL THEORY; GALERKIN METHODS; PRINCIPAL COMPONENT ANALYSIS;

AEROELASTIC ANALYSIS; DISCONTINUOUS GALERKIN; MULTI-INPUT , MULTI-OUTPUT SYSTEMS; PROPER ORTHOGONAL DECOMPOSITIONS; REDUCED ORDER MODELS; REDUCTION OF INPUTS; TIME AND FREQUENCY DOMAINS; TURBOMACHINERY APPLICATIONS;

COMPUTATIONAL FLUID DYNAMICS;

EID: 85088719097     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.2514/6.2005-4617     Document Type: Conference Paper

References (32)

1. Adamjan, V., Arov, D., and Krein, M., "Analytic Properties of Schmidt Pairs for a Hankel Operator and the Generalized Schur-Takagi Problem, " Math. USSR Sbornik, Vol. 15, 1971, pp. 31-73.
2. Bettayeb, M., Silverman, L., and Safonov, M., "Optimal Approximation of Continuous-Time Systems, " Proceedings of the 19th IEEE Conference on Decision and Control, Vol. 1, December 1980.
3. Kung, S.-Y. and Lin, D., "Optimal Hankel-Norm Model Reductions: Multivariable Systems, " IEEE Transactions on Automatic Control, Vol. AC-26, No. 1, August 1981, pp. 832-52.
4. Moore, B., "Principal component analysis in linear systems: controllability, observability, and model reduction, " IEEE Transactions on Automatic Control, Vol. AC-26, No. 1, August 1981, pp. 17-31.
5. Benner, P., Quintana-Orti, E., and Quintana-Orti, G., "State-space truncation methods for parallel model reduction of large-scale systems, " Proceedings of 43rd IEEE Conference on Decision and Control, 2004, pp. 3078-83.
6. Li, J. and White, J., "Low rank solution of Lyapunov equations, " SIAM Journal on Matrix Analysis and Applications, Vol. 24, No. 1, 2002, pp. 260-280.
7. Gugercin, S. and Antoulas, A., "A survey of model reduction by balanced truncation and some new results, " International Journal of Control, Vol. 77, 2004, pp. 748-766.
8. Sirovich, L., "Turbulence and the Dynamics of Coherent Structures. Part 1: Coherent Structures, " Quarterly of Applied Mathematics, Vol. 45, No. 3, October 1987, pp. 561-571.
9. Holmes, P., Lumley, J., and Berkooz, G., Turbulence, Coherent Structures, Dynamical Systems and Symmetry, Cambridge University Press, Cambridge, UK, 1996.
10. Romanowski, M., "Reduced Order Unsteady Aerodynamic and Aeroelastic Models using Karhunen-Loéve Eigenmodes, " AIAA Paper 96-194, 1996.
11. Dowell, E. and Hall, K., "Modeling of fluid-structure interaction, " Annual Review of Fluid Mechanics, Vol. 33, 2001, pp. 445-90.
12. Kunisch, K. and Volkwein, S., "Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics, " SIAM Journal on Numerical Analysis, Vol. 40, 2002, pp. 492-515.
13. Hinze, M. and Volkwein, S., "Proper Orthogonal Decomposition Surrogate Models for Nonlinear Dynamical Systems: Error Estimates and Suboptimal Control, " Tech. Rep. SFB609-Preprint-27-2004, Technische Universitat Dresden, 2004.
14. Kunisch, K. and Volkwein, S., "Control of Burgers' equation by reduced order approach using proper orthogonal decomposition, " Journal of Optimization Theory and Applications, Vol. 102, 1999, pp. 345-371.
15. Lall, S., M. J. and Glavaski, S., "A subspace approach to balanced truncation for model reduction of nonlinear control systems, " International Journal on Robust and Nonlinear Control, Vol. 12, 2002, pp. 519-535.
16. Willcox, K. and Peraire, J., "Balanced model reduction via the proper orthogonal decomposition, " AIAA Journal, Vol. 40, No. 11, November 2002, pp. 2223-2230.
17. Rowley, C. W., "Model reduction for fluids, using balanced proper orthogonal decomposition, " Int. J. on Bifurcation and Chaos (to appear), March 2005.
18. Darmofal, D. and Haimes, R., "Towards the next generation in CFD, " AIAA Paper 2005-0087, presented at the 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV January 10-13, 2005.
19. Cockburn, B. and Shu, C.-W., "Runge-Kutta discontinuous Galerkin methods for convection-dominated problems, " Journal of Scientific Computing, Vol. 16, No. 3, 2001, pp. 173-261.
20. Fidkowski, K. and Darmofal, D., "Development of a higher-order solver for aerodynamic applications, " AIAA Paper 2004-0436, presented at the 42nd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV January 5-8, 2004.
21. Roe, P., "Approximate Riemann solvers, parametric vectors, and difference schemes, " Journal of Computational Physics, Vol. 43, 1981, pp. 357-372.
22. Enns, D., Model Reduction for Control System Design, Ph.D. thesis, Department of Aeronautics & Astronautics, Stanford University, 1984.
23. Laub, A., Heath, M., Paige, C., and Ward, R., "Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms, " IEEE Transactions on Automatic Control, Vol. 32, No. 2, February 1987, pp. 115-122.
24. Kim, T., "Frequency-Domain Karhunen-Loeve method and Its Application to Linear Dynamic Systems, " AIAA Journal, Vol. 36, No. 11, November 1998, pp. 2117-2123.
25. Zhou, K., Salomon, G., and Wu, E., "Balanced Realization and model reduction for unstable systems, " Int. J. Robust Nonlinear Control, Vol. 9, 1999, pp. 183-198.
26. Newman, A. J., Modeling and Reduction with Application to Semiconductor Processing, Ph.D. thesis, University of Maryland, 1999.
27. Landon, R., "Compendium of unsteady aerodynamic measurements, " AGARD Report No. 702, August 1982.
28. Hall, K., A Linearized Euler Analysis of Unsteady Flows in Turbomachinery, Ph.D. thesis, Dept. of Aeronautics and Astronautics, MIT, May 1987.
29. Bolcs, A. and Fransson, T., "Aeroelasticity in Turbomachines; Comparison of Theoretical and Experimental Cascade Results, " Tech. Rep. AFOSR-TR-870605, Ecole Polytechnique Federale de Lausanne, 1986.
30. Atassi, H. and Akai, T., "Aerodynamic and aeroelastic characteristics of oscillating loaded cascades at low Mach number, " Trans. ASME, J. Eng. Power, Vol. 102, 1980, pp. 344-351.
31. Verdon, J. and Usab, W., "Application of a linearized unsteady aerodynamic analysis to standard cascade configurations, " NASA contractor report, 1985.
32. Fransson, T. and Verdon, J., "Standard Configurations for Unsteady Flow Through Vibrating Axial-Flow Turbomachine-Cascades, " Technical Report, Updated version, http://www.energy.kth.se/proj/projects/Markus%20Joecker/ STCF/default.htm, July 1991.