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Optimal mode decomposition for unsteady flows

Optimal mode decomposition for unsteady flows
Optimal mode decomposition for unsteady flows
A new method, herein referred to as optimal mode decomposition (OMD), of finding a linear model to describe the evolution of a fluid flow is presented. The method estimates the linear dynamics of a high-dimensional system which is first projected onto a subspace of a user-defined fixed rank. An iterative procedure is used to find the optimal combination of linear model and subspace that minimizes the system residual error. The OMD method is shown to be a generalization of dynamic mode decomposition (DMD), in which the subspace is not optimized but rather fixed to be the proper orthogonal decomposition (POD) modes. Furthermore, OMD is shown to provide an approximation to the Koopman modes and eigenvalues of the underlying system. A comparison between OMD and DMD is made using both a synthetic waveform and an experimental data set. The OMD technique is shown to have lower residual errors than DMD and is shown on a synthetic waveform to provide more accurate estimates of the system eigenvalues. This new method can be used with experimental and numerical data to calculate the ‘optimal’ low-order model with a user-defined rank that best captures the system dynamics of unsteady and turbulent flows.

computational methods, low-dimensional models, nonlinear dynamical systems
0022-1120
473-503
Wynn, A.
ca41e493-9961-49e8-aad2-66e7d6fc2e84
Pearson, D.S.
6bb65bfe-346b-4cae-9afd-d2dd05342607
Ganapathisubramani, B.
5e69099f-2f39-4fdd-8a85-3ac906827052
Goulart, P. J.
7f978318-3997-459a-8b27-9e60f03d0ebd
Wynn, A.
ca41e493-9961-49e8-aad2-66e7d6fc2e84
Pearson, D.S.
6bb65bfe-346b-4cae-9afd-d2dd05342607
Ganapathisubramani, B.
5e69099f-2f39-4fdd-8a85-3ac906827052
Goulart, P. J.
7f978318-3997-459a-8b27-9e60f03d0ebd

Wynn, A., Pearson, D.S., Ganapathisubramani, B. and Goulart, P. J. (2013) Optimal mode decomposition for unsteady flows. Journal of Fluid Mechanics, 733, 473-503. (doi:10.1017/jfm.2013.426).

Record type: Article

Abstract

A new method, herein referred to as optimal mode decomposition (OMD), of finding a linear model to describe the evolution of a fluid flow is presented. The method estimates the linear dynamics of a high-dimensional system which is first projected onto a subspace of a user-defined fixed rank. An iterative procedure is used to find the optimal combination of linear model and subspace that minimizes the system residual error. The OMD method is shown to be a generalization of dynamic mode decomposition (DMD), in which the subspace is not optimized but rather fixed to be the proper orthogonal decomposition (POD) modes. Furthermore, OMD is shown to provide an approximation to the Koopman modes and eigenvalues of the underlying system. A comparison between OMD and DMD is made using both a synthetic waveform and an experimental data set. The OMD technique is shown to have lower residual errors than DMD and is shown on a synthetic waveform to provide more accurate estimates of the system eigenvalues. This new method can be used with experimental and numerical data to calculate the ‘optimal’ low-order model with a user-defined rank that best captures the system dynamics of unsteady and turbulent flows.

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More information

Published date: October 2013
Keywords: computational methods, low-dimensional models, nonlinear dynamical systems
Organisations: Aeronautics, Astronautics & Comp. Eng, Aerodynamics & Flight Mechanics Group, Faculty of Engineering and the Environment

Identifiers

Local EPrints ID: 359353
URI: http://eprints.soton.ac.uk/id/eprint/359353
ISSN: 0022-1120
PURE UUID: 943e5679-6d4c-40a8-9aeb-fb90bf9c923c
ORCID for B. Ganapathisubramani: ORCID iD orcid.org/0000-0001-9817-0486

Catalogue record

Date deposited: 28 Oct 2013 16:39
Last modified: 03 Dec 2019 01:41

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