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Main Title: Recursive dynamic mode decomposition of transient and post-transient wake flows
Author(s): Noack, Bernd R.
Stankiewicz, Witold
Morzyński, Marek
Schmid, Peter J.
Type: Article
Language Code: en
Abstract: A novel data-driven modal decomposition of fluid flow is proposed, comprising key features of proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD). The first mode is the normalized real or imaginary part of the DMD mode that minimizes the time-averaged residual. The Nth mode is defined recursively in an analogous manner based on the residual of an expansion using the first N - 1 modes. The resulting recursive DMD (RDMD) modes are orthogonal by construction, retain pure frequency content and aim at low residual. Recursive DMD is applied to transient cylinder wake data and is benchmarked against POD and optimized DMD (Chen et al., J. Nonlinear Sci., vol. 22, 2012, pp. 887–915) for the same snapshot sequence. Unlike POD modes, RDMD structures are shown to have purer frequency content while retaining a residual of comparable order to POD. In contrast to DMD, with exponentially growing or decaying oscillatory amplitudes, RDMD clearly identifies initial, maximum and final fluctuation levels. Intriguingly, RDMD outperforms both POD and DMD in the limit-cycle resolution from the same snapshots. Robustness of these observations is demonstrated for other parameters of the cylinder wake and for a more complex wake behind three rotating cylinders. Recursive DMD is proposed as an attractive alternative to POD and DMD for empirical Galerkin models, in particular for nonlinear transient dynamics.
Issue Date: 2016
Date Available: 27-Oct-2017
DDC Class: 530 Physik
Subject(s): low-dimensional models
Sponsor/Funder: DFG, SFB 880, Grundlagen des Hochauftriebs künftiger Verkehrsflugzeuge
Journal Title: Journal of fluid mechanics
Publisher: Cambridge University Press
Publisher Place: Cambridge
Volume: 809
Publisher DOI: 10.1017/jfm.2016.678
Page Start: 843
Page End: 872
EISSN: 1469-7645
ISSN: 0022-1120
Notes: Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.
This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.
Appears in Collections:FG Experimentelle Strömungsmechanik » Publications

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