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 iter...

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Vydané v:Journal of fluid mechanics Ročník 733; s. 473 - 503
Hlavní autori: Wynn, A., Pearson, D. S., Ganapathisubramani, B., Goulart, P. J.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Cambridge, UK Cambridge University Press 25.10.2013
Predmet:
Boundary layer and shear turbulence
Computational fluid dynamics
Computational mathematics
Computational methods in fluid dynamics
Decomposition
Dynamical systems
Dynamics
Exact sciences and technology
Fluid dynamics
Fluid flow
Fluid mechanics
Fundamental areas of phenomenology (including applications)
Mathematical models
Optimization
Physics
Subspaces
Turbulence
Turbulent flows, convection, and heat transfer
computational methods
nonlinear dynamical systems
low-dimensional models
Turbulent flow
Computational fluid dynamics
Orthogonal function
Digital simulation
Eigenfunctions
Modelling
Unsteady flow
Step
Nonlinear dynamical systems
Boundary layers
ISSN:0022-1120, 1469-7645
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Popis
Shrnutí: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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ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2013.426