Adaptive panel representation for 3D vortex ring motion and instability (Q936182)

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.