Krueger Paul S, Hahsler Michael, Olinick Eli V, Williams Sheila H, Zharfa Mohammadreza
Department of Mechanical Engineering, Information, and Systems, Southern Methodist University, Dallas, TX 75275, USA.
Department of Engineering Management, Information, and Systems, Southern Methodist University, Dallas, TX 75275, USA.
Proc Math Phys Eng Sci. 2019 Aug;475(2228):20180897. doi: 10.1098/rspa.2018.0897. Epub 2019 Aug 21.
Vortical flow patterns generated by swimming animals or flow separation (e.g. behind bluff objects such as cylinders) provide important insight to global flow behaviour such as fluid dynamic drag or propulsive performance. The present work introduces a new method for quantitatively comparing and classifying flow fields using a novel graph-theoretic concept, called a weighted Gabriel graph, that employs critical points of the velocity vector field, which identify key flow features such as vortices, as graph vertices. The edges (connections between vertices) and edge weights of the weighted Gabriel graph encode local geometric structure. The resulting graph exhibits robustness to minor changes in the flow fields. Dissimilarity between flow fields is quantified by finding the best match (minimum difference) in weights of matched graph edges under relevant constraints on the properties of the edge vertices, and flows are classified using hierarchical clustering based on computed dissimilarity. Application of this approach to a set of artificially generated, periodic vortical flows demonstrates high classification accuracy, even for large perturbations, and insensitivity to scale variations and number of periods in the periodic flow pattern. The generality of the approach allows for comparison of flows generated by very different means (e.g. different animal species).
由游动动物产生的涡旋流模式或流动分离（例如在诸如圆柱体等钝体后面）为诸如流体动力阻力或推进性能等整体流动行为提供了重要见解。本研究介绍了一种新方法，该方法使用一种名为加权加布里埃尔图的新颖图论概念对流场进行定量比较和分类，该概念将速度矢量场的临界点用作图的顶点，这些临界点可识别诸如涡旋等关键流动特征。加权加布里埃尔图的边（顶点之间的连接）和边权重编码局部几何结构。所得的图对流场的微小变化具有鲁棒性。通过在边顶点属性的相关约束下找到匹配图边权重的最佳匹配（最小差异）来量化流场之间的差异，并使用基于计算出的差异的层次聚类对流进行分类。将该方法应用于一组人工生成的周期性涡旋流，即使对于大扰动也显示出高分类精度，并且对周期性流模式中的尺度变化和周期数不敏感。该方法的通用性允许比较通过非常不同的方式（例如不同动物物种）产生的流。
