Adaptive panel representation for 3D vortex ring motion and instability
type: Item
instance of: scholarly article
title: Adaptive panel representation for 3D vortex ring motion and instability
zbMATH Open document ID: 1233.76083
DOI: 10.1155/2007/68953
author: Leon Kaganovskiy
published in: Mathematical Problems in Engineering
publication date: 2008-08-13T00:00:00Z
full work available at URL: https://eudml.org/doc/45223
review text: Summary: We develop a hierarchical panel method for representing vortex sheet surface motion in 3D flows. Unlike previously employed filament methods, each panel is a leaf of the tree, so it can be subdivided locally, which allows for an efficient adaptive point insertion. In addition, we develop curvature-based insertion criteria which allow to localize point insertion to the most complicated curved regions of the sheet. The particles representing the sheet are advected by a regularized Biot-Savart integral with Rosenhead-Moore kernel. The particle velocities are evaluated by an adaptive tree-code algorithm based on Taylor expansions in Cartesian coordinates due to \textit{K. Lindsay} and \textit{R. Krasny} [J. Comput. Phys. 172, No.~2, 879--907 (2001; Zbl 1002.76093)]. The method allows to consider much later stages of a vortex ring instability, which may shed light on this complicated flow phase directly leading to the turbulent flow.
Mathematics Subject Classification ID: 76M25
Mathematics Subject Classification ID: 76B47
zbMATH DE Number: 5311257
zbMATH Keywords: vortex sheet
zbMATH Keywords: adaptive point insertion
zbMATH Keywords: regularized Biot-Savart integral
zbMATH Keywords: adaptive tree-code algorithm
MaRDI profile type: Publication
OpenAlex ID: W2010554412
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description: scientific article; zbMATH DE number 5311257