On the accuracy of dynamic mode decomposition in estimating instability of wave packet

On the accuracy of dynamic mode decomposition in estimating instability of wave packet Lots of unstable flows in both nature and engineering pose multi-scale perturbations with infinitesimal initial amplitude, which compete and interact with each other during their unstable evolution. Dynamic mode decomposition (DMD) analysis can be used to extract these components’ temporal/spatial growth rate. Therefore, it is necessary to evaluate the accuracy performance and confidence limit of DMD algorithm in the circumstance of multi-scale instability wave packet. In the present study, we use a linear combination of a sinusoidal unstable wave and its high-order harmonics as a prototype, based on which an error analysis of DMD algorithm is taken. In first, different numerical algorithms of DMD analysis are compared in terms of both accuracy and efficiency. The accuracy evaluation of the classical DMD algorithm in a large parameter domain is followed. It is found that the superimposition of finer structures with less energy dominance might damage the estimation accuracy of the primary structures’ growth rate. Strong evidences suggest that even in a linear circumstance, resolving the dynamics of small-scale structures is comparably more difficult than that of the primary structures, i.e., DMD algorithm has a preference for structures with energetic dominance. Finally, the recommended thresholds for the sampling/discretizing parameters are summarized for practical usage. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Experiments in Fluids Springer Journals

On the accuracy of dynamic mode decomposition in estimating instability of wave packet

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2015 by Springer-Verlag Berlin Heidelberg
Subject
Engineering; Engineering Fluid Dynamics; Fluid- and Aerodynamics; Engineering Thermodynamics, Heat and Mass Transfer
ISSN
0723-4864
eISSN
1432-1114
D.O.I.
10.1007/s00348-015-2015-6
Publisher site
See Article on Publisher Site

Abstract

Lots of unstable flows in both nature and engineering pose multi-scale perturbations with infinitesimal initial amplitude, which compete and interact with each other during their unstable evolution. Dynamic mode decomposition (DMD) analysis can be used to extract these components’ temporal/spatial growth rate. Therefore, it is necessary to evaluate the accuracy performance and confidence limit of DMD algorithm in the circumstance of multi-scale instability wave packet. In the present study, we use a linear combination of a sinusoidal unstable wave and its high-order harmonics as a prototype, based on which an error analysis of DMD algorithm is taken. In first, different numerical algorithms of DMD analysis are compared in terms of both accuracy and efficiency. The accuracy evaluation of the classical DMD algorithm in a large parameter domain is followed. It is found that the superimposition of finer structures with less energy dominance might damage the estimation accuracy of the primary structures’ growth rate. Strong evidences suggest that even in a linear circumstance, resolving the dynamics of small-scale structures is comparably more difficult than that of the primary structures, i.e., DMD algorithm has a preference for structures with energetic dominance. Finally, the recommended thresholds for the sampling/discretizing parameters are summarized for practical usage.

Journal

Experiments in FluidsSpringer Journals

Published: Aug 4, 2015

References

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