Adaptive Panel Representation for 3D Vortex Ring Motion and Instability

A hierarchical panel method for representing vortex sheet surface motion in 3D flow is presented. Unlike previously employed filament methods, each panel is a leaf of the tree, so it can be subdivided locally, which allows an efficient adaptive point insertion. In addition, we developed 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 treecode algorithm based on Taylor expansions in Cartesian coordinates due to Lindsay and Krasny (2001). 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