Trajectory-based computational study of coherent behavior in flows

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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)
Original languageEnglish
JournalProceedings in applied mathematics and mechanics
Volume17
Issue number1
Pages (from-to)11-14
Number of pages4
ISSN1617-7061
DOIs
Publication statusPublished - 12.2017
Event88th Annual Meeting of the International Association of Applied Mathematics and Mechanics - GAMM 2017 - Weimar, Germany
Duration: 06.03.201710.03.2017
Conference number: 88
https://jahrestagung.gamm-ev.de/index.php/2017/annual-meeting-2017

Bibliographical note

Volume 17 (2017) of PAMM “Proceedings in Applied Mathematics and Mechanics” assembles the contributions to the 88th Annual Meeting of the Gesellschaft für Angewandte Mathematik und Mechanik (GAMM), held 6 – 10 March 2017 at Weimar, Germany, supported by Bauhaus‐Universität Weimar and Technische Universität Ilmenau.

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