Year: 2023
Author: Wai Ming Chau, Shingyu Leung
Communications in Computational Physics, Vol. 33 (2023), Iss. 3 : pp. 824–848
Abstract
We propose a clustering-based approach for identifying coherent flow structures in continuous dynamical systems. We first treat a particle trajectory over a finite time interval as a high-dimensional data point and then cluster these data from different initial locations into groups. The method then uses the normalized standard deviation or mean absolute deviation to quantify the deformation. Unlike the usual finite-time Lyapunov exponent (FTLE), the proposed algorithm considers the complete traveling history of the particles. We also suggest two extensions of the method. To improve the computational efficiency, we develop an adaptive approach that constructs different subsamples of the whole particle trajectory based on a finite time interval. To start the computation in parallel to the flow trajectory data collection, we also develop an on-the-fly approach to improve the solution as we continue to provide more measurements for the algorithm. The method can efficiently compute the WCVE over a different time interval by modifying the available data points.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/ 10.4208/cicp.OA-2022-0177
Communications in Computational Physics, Vol. 33 (2023), Iss. 3 : pp. 824–848
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Dynamical system visualization finite time Lyapunov exponent numerical methods for differential equations k-means clustering.