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Randomized methods to characterize large-scale vortical flow networks


Autoři: Zhe Bai aff001;  N. Benjamin Erichson aff002;  Muralikrishnan Gopalakrishnan Meena aff003;  Kunihiko Taira aff003;  Steven L. Brunton aff004
Působiště autorů: Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA, United States of America aff001;  Department of Applied Mathematics, University of Washington, Seattle, WA, United States of America aff002;  Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA, United States of America aff003;  Department of Mechanical Engineering, University of Washington, Seattle, WA, United States of America aff004
Vyšlo v časopise: PLoS ONE 14(11)
Kategorie: Research Article
doi: https://doi.org/10.1371/journal.pone.0225265

Souhrn

We demonstrate the effective use of randomized methods for linear algebra to perform network-based analysis of complex vortical flows. Network theoretic approaches can reveal the connectivity structures among a set of vortical elements and analyze their collective dynamics. These approaches have recently been generalized to analyze high-dimensional turbulent flows, for which network computations can become prohibitively expensive. In this work, we propose efficient methods to approximate network quantities, such as the leading eigendecomposition of the adjacency matrix, using randomized methods. Specifically, we use the Nyström method to approximate the leading eigenvalues and eigenvectors, achieving significant computational savings and reduced memory requirements. The effectiveness of the proposed technique is demonstrated on two high-dimensional flow fields: two-dimensional flow past an airfoil and two-dimensional turbulence. We find that quasi-uniform column sampling outperforms uniform column sampling, while both feature the same computational complexity.

Klíčová slova:

Centrality – Eigenvalues – Eigenvectors – Flow field – Fluid flow – Linear algebra – Turbulence – Singular value decomposition


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