Trajectory-based computational study of coherent behavior in flows
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In: Proceedings in applied mathematics and mechanics, Vol. 17, No. 1, 12.2017, p. 11-14.
Research output: Journal contributions › Journal articles › Research › peer-review
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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 -