Journal ArticleDOI
A hierarchy of low-dimensional models for the transient and post-transient cylinder wake
TLDR
A hierarchy of low-dimensional Galerkin models is proposed for the viscous, incompressible flow around a circular cylinder building on the pioneering works of Stuart (1958), Deane et al. (1991), and Ma & Karniadakis (2002) as mentioned in this paper.Abstract:
A hierarchy of low-dimensional Galerkin models is proposed for the viscous, incompressible flow around a circular cylinder building on the pioneering works of Stuart (1958), Deane et al. (1991), and Ma & Karniadakis (2002). The empirical Galerkin model is based on an eight-dimensional Karhunen–Loeve decomposition of a numerical simulation and incorporates a new ‘shift-mode’ representing the mean-field correction. The inclusion of the shift-mode significantly improves the resolution of the transient dynamics from the onset of vortex shedding to the periodic von Karman vortex street. In addition, the Reynolds-number dependence of the flow can be described with good accuracy. The inclusion of stability eigenmodes further enhances the accuracy of fluctuation dynamics. Mathematical and physical system reduction approaches lead to invariant-manifold and to mean-field models, respectively. The corresponding two-dimensional dynamical systems are further reduced to the Landau amplitude equation.read more
Citations
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Dynamic mode decomposition of numerical and experimental data
TL;DR: In this article, a method is introduced that is able to extract dynamic information from flow fields that are either generated by a (direct) numerical simulation or visualized/measured in a physical experiment.
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Discovering governing equations from data by sparse identification of nonlinear dynamical systems
TL;DR: This work develops a novel framework to discover governing equations underlying a dynamical system simply from data measurements, leveraging advances in sparsity techniques and machine learning and using sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data.
Journal ArticleDOI
Spectral analysis of nonlinear flows
TL;DR: In this article, a technique for describing the global behaviour of complex nonlinear flows by decomposing the flow into modes determined from spectral analysis of the Koopman operator, an infinite-dimensional linear operator associated with the full nonlinear system, is presented.
Journal Article
Spectral analysis of nonlinear flows
TL;DR: In this article, a technique for describing the global behaviour of complex nonlinear flows by decomposing the flow into modes determined from spectral analysis of the Koopman operator, an infinite-dimensional linear operator associated with the full nonlinear system, is presented.
Journal ArticleDOI
On dynamic mode decomposition: Theory and applications
TL;DR: In this paper, the authors define dynamic mode decomposition (DMD) as the eigendecomposition of an approximating linear operator, and propose sampling strategies that increase computational efficiency and mitigate the effects of noise.
References
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TL;DR: In this article, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
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Vortex Dynamics in the Cylinder Wake
TL;DR: A review of wake vortex dynamics can be found in this article, with a focus on the three-dimensional aspects of nominally two-dimensional wake flows, as well as the discovery of several new phenomena in wakes.
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TL;DR: In this article, the authors present a review of rigor properties of low-dimensional models and their applications in the field of fluid mechanics. But they do not consider the effects of random perturbation on models.
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TL;DR: In this article, the dynamique des : fluides, equations : differentielles, analyse, elements : finis, stabilite, stationnaire, mathematiques, methodes, numeriques, etc.