A Voronoi-tessellation-based approach for detection of coherent structures in sparsely-seeded flows

Abstract

A robust algorithm to detect coherent structures with sparse Lagrangian particle tracking data, using Voronoi tessellation and techniques from spectral graph theory, is proposed and tested. Neighbouring tracer particles are naturally identified through the Voronoi tessellation of the tracers' distribution. The method examines the neighbouring time of tracer trajectories, defined as the total flow time two Voronoi cells share a common Voronoi edge, by converting this information into a Cartesian distance in the graph representation of the Voronoi diagram. Coherence is assigned to groups of Voronoi cells whose neighbouring time remains high throughout the time interval of analysis. The technique is first tested on the two-dimensional synthetic data of a double-gyre flow, and then with challenging, large-scale three-dimensional Lagrangian particle tracking data behind a bluff body at high Reynolds number. The novel approach proves to be successful at identifying coherence with realistic and very sparse experimental data. Specifically, it is shown for the first time that coherent structures are identifiable for mean inter-particle distances of the order of the largest length scales in the flow.

Bayesian random persistence diagram generation: An application to material microstructure analysis

“…, p n }. We use V to construct a Voronoi tessellation of the wedge W [23] and utilize the area of the resulting tiles to define the spatial pattern function. Formally, let R i be the tile generated by p i via the Voronoi tessellation of W generated using V .…”