Long Time Computation of Two-Dimensional Vortex Sheet by Point Vortex Method

Abstract

Two-dimensional vortex sheet suffers an unstable deformation from the Kelvin–Helmholtz instability and a curvature singularity which develops in a finite time. In this paper, long time computations of the two-dimensional vortex sheet are performed by a robust and efficient numerical method with high accuracy. To handle the rapid and non-uniform stretching of the interface, we adopt the adaptive point insertion and redistribution procedures. Computational results show highly refined structures of a complex and chaotic pattern for the vortex sheet up to very long time.