Trajectory‐based computational study of coherent behavior in flows

Trajectory‐based computational study of coherent behavior in flows The notion of coherence in time‐dependent dynamical systems is used to describe mobile sets that do not freely mix with the surrounding regions in phase space. In particular, coherent behavior has an impact on transport and mixing processes in fluid flows. The mathematical definition and numerical study of coherent structures in flows has received considerable scientific interest for about two decades. However, mathematically sound methodologies typically require full knowledge of the flow field or at least high resolution trajectory data, which may not be available in applications. Recently, different computational methods have been proposed to identify coherent behavior in flows directly from Lagrangian trajectory data, such as obtained from particle tracking algorithms. In this context, spatio‐temporal clustering algorithms have been proven to be very effective for the extraction of coherent sets from sparse and possibly incomplete trajectory data. Inspired by these recent approaches, we consider an unweighted, undirected network, in which Lagrangian particle trajectories serve as network nodes. A link is established between two nodes if the respective trajectories come close to each other at least once in the course of time. Classical graph algorithms are then employed to analyze the resulting network. In particular, spectral graph partitioning schemes allow us to extract coherent sets of the underlying flow. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Proceedings in Applied Mathematics & Mechanics Wiley

Trajectory‐based computational study of coherent behavior in flows

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
Copyright © 2017 Wiley Subscription Services
ISSN
1617-7061
eISSN
1617-7061
D.O.I.
10.1002/pamm.201710004
Publisher site
See Article on Publisher Site

Abstract

The notion of coherence in time‐dependent dynamical systems is used to describe mobile sets that do not freely mix with the surrounding regions in phase space. In particular, coherent behavior has an impact on transport and mixing processes in fluid flows. The mathematical definition and numerical study of coherent structures in flows has received considerable scientific interest for about two decades. However, mathematically sound methodologies typically require full knowledge of the flow field or at least high resolution trajectory data, which may not be available in applications. Recently, different computational methods have been proposed to identify coherent behavior in flows directly from Lagrangian trajectory data, such as obtained from particle tracking algorithms. In this context, spatio‐temporal clustering algorithms have been proven to be very effective for the extraction of coherent sets from sparse and possibly incomplete trajectory data. Inspired by these recent approaches, we consider an unweighted, undirected network, in which Lagrangian particle trajectories serve as network nodes. A link is established between two nodes if the respective trajectories come close to each other at least once in the course of time. Classical graph algorithms are then employed to analyze the resulting network. In particular, spectral graph partitioning schemes allow us to extract coherent sets of the underlying flow. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Journal

Proceedings in Applied Mathematics & MechanicsWiley

Published: Jan 1, 2017

References

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