K. Lindsay et R. Krasny, A particle method and adaptive treecode for vortex sheet motion in three-dimensional flow, J COMPUT PH, 172(2), 2001, pp. 879-907
A particle method is presented for computing vortex sheet motion in three-d
imensional flow. The particles representing the sheet are advected by a reg
ularized Biot-Savart integral in which the exact singular kernel is replace
d by the Rosenhead-Moore kernel. New particles are inserted to maintain res
olution as the sheet rolls up. The particle velocities are evaluated by an
adaptive treecode algorithm based on Taylor approximation in Cartesian coor
dinates, and the necessary Taylor coefficients are computed by a recurrence
relation. The adaptive features include a divide-and-conquer evaluation st
rategy, nonuniform rectangular clusters, variable-order approximation, and
a run-time choice between Taylor approximation and direct summation. Tests
are performed to document the treecode's accuracy and efficiency. The metho
d is applied to simulate the roll-up of a circular-disk vortex sheet into a
vortex ring. Two examples are presented, azimuthal waves on a vortex ring
and the merger of two vortex rings. (C) 2001 Academic Press.