Simple and efficient numerical methods for vortex sheet motion with surface tension

Abstract

We present two simple and efficient explicit methods for the vortex sheet with surface tension. The first one is the standard point vortex method, which has been known to be unstable in the presence of surface tension, due to spurious growth of waves of high modes. We show, for the first time, that the standard point vortex method is able to calculate the vortex sheet motion with surface tension by employing a Fourier filtering. The second method is a modification of the Pullin method using central differences for numerical differentiations. This method is more convenient to implement than other spectral methods and is free from the aliasing instability. We give a linear stability analysis for the numerical methods and show results for the long-time evolution of the vortex sheet. We also propose a new redistribution procedure to control point clustering, by setting limits of minimum and maximum distances between neighboring points. This procedure is found to be very efficient for long-time computations of the explicit methods. Copyright (c) 2013 John Wiley & Sons, Ltd.