Trajectory-based computational study of coherent behavior in flows

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Trajectory-based computational study of coherent behavior in flows. / Padberg-Gehle, Kathrin; Schneide, Christiane.
In: Proceedings in applied mathematics and mechanics, Vol. 17, No. 1, 12.2017, p. 11-14.

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@article{cfa92db2ff8243a3a7f0ef68a8449ca6,
title = "Trajectory-based computational study of coherent behavior in flows",
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. ({\textcopyright} 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)",
keywords = "Mathematics",
author = "Kathrin Padberg-Gehle and Christiane Schneide",
note = "Volume 17 (2017) of PAMM “Proceedings in Applied Mathematics and Mechanics” assembles the contributions to the 88th Annual Meeting of the Gesellschaft f{\"u}r Angewandte Mathematik und Mechanik (GAMM), held 6 – 10 March 2017 at Weimar, Germany, supported by Bauhaus‐Universit{\"a}t Weimar and Technische Universit{\"a}t Ilmenau. ; 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics - GAMM 2017, GAMM 2017 ; Conference date: 06-03-2017 Through 10-03-2017",
year = "2017",
month = dec,
doi = "10.1002/pamm.201710004",
language = "English",
volume = "17",
pages = "11--14",
journal = "Proceedings in applied mathematics and mechanics",
issn = "1617-7061",
publisher = "Wiley-VCH Verlag",
number = "1",
url = "https://jahrestagung.gamm-ev.de/index.php/2017/annual-meeting-2017",

}

RIS

TY - JOUR

T1 - Trajectory-based computational study of coherent behavior in flows

AU - Padberg-Gehle, Kathrin

AU - Schneide, Christiane

N1 - Conference code: 88

PY - 2017/12

Y1 - 2017/12

N2 - 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)

AB - 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)

KW - Mathematics

U2 - 10.1002/pamm.201710004

DO - 10.1002/pamm.201710004

M3 - Journal articles

VL - 17

SP - 11

EP - 14

JO - Proceedings in applied mathematics and mechanics

JF - Proceedings in applied mathematics and mechanics

SN - 1617-7061

IS - 1

T2 - 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics - GAMM 2017

Y2 - 6 March 2017 through 10 March 2017

ER -

DOI