Topology‐Preserving λ₂‐based Vortex Core Line Detection for Flow Visualization

Abstract

We propose a novel vortex core line extraction method based on the λ 2 vortex region criterion in order to improve the detection of vortex features for 3D flow visualization. The core line is defined as a curve that connects λ 2 minima restricted to planes that are perpendicular to the core line. The basic algorithm consists of the following stages: (1) λ 2 field construction and isosurface extraction; (2) computation of the curve skeleton of the λ 2 isosurface to build an initial prediction for the core line; (3) correction of the locations of the prediction by searching for λ 2 minima on planes perpendicular to the core line. In particular, we consider the topology of the vortex core lines, guaranteeing the same topology as the initial curve skeleton. Furthermore, we propose a geometry-guided definition of vortex bifurcation, which represents the split of one core line into two parts. Finally, we introduce a user-guided approach in order to narrow down vortical regions taking into account the graph of λ 2 along the computed vortex core line. We demonstrate the effectiveness of our method by comparing our results to previous core line detection methods with both simulated and experimental data; in particular, we show robustness of our method for noise-affected data.

Vortex core detection: back to basics

“…The main idea is shown in Figure 2, and is similar to the horse-shoe vortex shown in Schafhitzel et al 9 The flow is easy to describe, although the equations are a bit complicated. Some software is available on the Internet.…”

“…This phenomenon was exhibited in a steady flow, but obviously anything that happens in a steady flow can also happen in an unsteady flow. Schafhitzel et al 9 evaluate several higher-order methods empirically.…”

Semi-Automatic Vortex Extraction in 4D PC-MRI Cardiac Blood Flow Data using Line Predicates

“…This might amplify noise in the data and introduce further errors. We found that the λ 2 -criterion is more established among blood flowspecific works [4,36,39] and decided to use it as well. The necessary eigenvalue analysis of the Jacobian matrix is done on the GPU using Cardano's method [21].…”

“…[19], the Q-criterion by Hunt [18], the reduced velocity by Sujudi and Haimes [40], cores of swirling particle motion by Weinkauf et al [45], normalized helicity by Levy et al [23], vorticity and torsion. Schafhitzel et al state that the λ 2 -criterion is most effective and most reliable [36]. Global algorithms return more precise results to the price of higher computation times.…”

Visualization and Analysis of Vortex-Turbine Intersections in Wind Farms

“…An alternative approach to finding extremal lines of vortices following (minimal) pressure scalars and vorticity vectors, named the "predictor-corrector" technique, was developed by Singer and Banks [19], [20], [21]. It was extended by Ertl et al [3], [22], [23], [24], where the 2 criterion is used instead of pressure, and vorticity vectors are retained for vortex directions.…”