Reduced-order models for flow control: Balanced models and Koopman modes

Clarence W. Rowley; Igor Mezić; Shervin Bagheri; Philipp Schlatter; Dan S. Henningson

doi:10.1007/978-90-481-3723-7_6

Reduced-order models for flow control: Balanced models and Koopman modes

Clarence W. Rowley, Igor Mezić, Shervin Bagheri, Philipp Schlatter, Dan S. Henningson

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

20 Scopus citations

Abstract

This paper addresses recent developments in model-reduction techniques applicable to fluid flows. The main goal is to obtain low-order models tractable enough to be used for analysis and design of feedback laws for flow control, while retaining the essential physics. We first give a brief overview of several model reduction techniques, including Proper Orthogonal Decomposition [3], balanced truncation [8, 9], and the related Eigensystem Realization Algorithm [5, 6], and discuss strengths and weaknesses of each approach. We then describe a new method for analyzing nonlinear flows based on spectral analysis of the Koopman operator, a linear operator defined for any nonlinear dynamical system. We show that, for an example of a jet in crossflow, the resulting Koopman modes decouple the dynamics at different timescales more effectively than POD modes, and capture the relevant frequencies more accurately than linear stability analysis.

Original language	English (US)
Title of host publication	7th IUTAM Symposium on Laminar-Turbulent Transition - Proceedings of the 7th IUTAM Symposium on Laminar-Turbulent Transition
Publisher	Springer Verlag
Pages	43-50
Number of pages	8
ISBN (Print)	9789048137220
DOIs	https://doi.org/10.1007/978-90-481-3723-7_6
State	Published - 2010
Event	7th IUTAM Symposium on Laminar-Turbulent Transition - Stockholm, Sweden Duration: Jun 23 2009 → Jun 26 2009

Publication series

Name	IUTAM Bookseries
Volume	18
ISSN (Print)	1875-3507

Other

Other	7th IUTAM Symposium on Laminar-Turbulent Transition
Country/Territory	Sweden
City	Stockholm
Period	6/23/09 → 6/26/09

All Science Journal Classification (ASJC) codes

Civil and Structural Engineering
Automotive Engineering
Aerospace Engineering
Acoustics and Ultrasonics
Mechanical Engineering

Access to Document

10.1007/978-90-481-3723-7_6

Cite this

Rowley, C. W., Mezić, I., Bagheri, S., Schlatter, P., & Henningson, D. S. (2010). Reduced-order models for flow control: Balanced models and Koopman modes. In 7th IUTAM Symposium on Laminar-Turbulent Transition - Proceedings of the 7th IUTAM Symposium on Laminar-Turbulent Transition (pp. 43-50). (IUTAM Bookseries; Vol. 18). Springer Verlag. https://doi.org/10.1007/978-90-481-3723-7_6

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abstract = "This paper addresses recent developments in model-reduction techniques applicable to fluid flows. The main goal is to obtain low-order models tractable enough to be used for analysis and design of feedback laws for flow control, while retaining the essential physics. We first give a brief overview of several model reduction techniques, including Proper Orthogonal Decomposition [3], balanced truncation [8, 9], and the related Eigensystem Realization Algorithm [5, 6], and discuss strengths and weaknesses of each approach. We then describe a new method for analyzing nonlinear flows based on spectral analysis of the Koopman operator, a linear operator defined for any nonlinear dynamical system. We show that, for an example of a jet in crossflow, the resulting Koopman modes decouple the dynamics at different timescales more effectively than POD modes, and capture the relevant frequencies more accurately than linear stability analysis.",

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Rowley, CW, Mezić, I, Bagheri, S, Schlatter, P & Henningson, DS 2010, Reduced-order models for flow control: Balanced models and Koopman modes. in 7th IUTAM Symposium on Laminar-Turbulent Transition - Proceedings of the 7th IUTAM Symposium on Laminar-Turbulent Transition. IUTAM Bookseries, vol. 18, Springer Verlag, pp. 43-50, 7th IUTAM Symposium on Laminar-Turbulent Transition, Stockholm, Sweden, 6/23/09. https://doi.org/10.1007/978-90-481-3723-7_6

Reduced-order models for flow control: Balanced models and Koopman modes. / Rowley, Clarence W.; Mezić, Igor; Bagheri, Shervin et al.
7th IUTAM Symposium on Laminar-Turbulent Transition - Proceedings of the 7th IUTAM Symposium on Laminar-Turbulent Transition. Springer Verlag, 2010. p. 43-50 (IUTAM Bookseries; Vol. 18).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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Reduced-order models for flow control: Balanced models and Koopman modes

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