Adaptive panel representation for 3D vortex ring motion and instability.

*(English)*Zbl 1233.76083Summary: 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 K. Lindsay and 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.

##### MSC:

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

76B47 | Vortex flows for incompressible inviscid fluids |

##### Keywords:

vortex sheet; adaptive point insertion; regularized Biot-Savart integral; adaptive tree-code algorithm
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\textit{L. Kaganovskiy}, Math. Probl. Eng. 2007, Article ID 68953, 22 p. (2007; Zbl 1233.76083)

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