Almost optimal convergence of the point vortex method for vortex sheets using numerical filtering

Almost optimal convergence of the point vortex method for vortex sheets using numerical filtering

Standard numerical methods for the Birkhoff-Rott equation for a vortex sheet are unstable due to the amplification of roundoff error by the Kelvin-Helmholtz instability. A nonlinear filtering method was used by Krasny to eliminate this spurious growth of round-off error and accurately compute the Birkhoff-Rott solution essentially up to the time it becomes singular. In this paper convergence is...

Numerical Convergence of the Random Vortex Method for Complex Flows

Vortex methods rely principally on a discretization of the continuous two-dimensional time dependent vorticity eld into a large number of vortex \blobs", whose position and strength determine the underlying velocity eld. In this paper, the convergence of the random vortex method (RVM) for a complex ow is studied in function of three discretization parameters. Two of these parameters are related...

Convergence of the point vortex method for 2-D vortex sheet

We give an elementary proof of the convergence of the point vortex method (PVM) to a classical weak solution for the two-dimensional incompressible Euler equations with initial vorticity being a finite Radon measure of distinguished sign and the initial velocity of locally bounded energy. This includes the important example of vortex sheets, which exhibits the classical Kelvin-Helmholtz instabi...

Convergence of the Point Vortex Methodfor 2 - D Vortex

We give an elementary proof of the convergence of the point vor-tex method (PVM) to a classical weak solution for the two-dimensional incom-pressible Euler equations with initial vorticity being a nite Radon measure of distinguished sign and the initial velocity of locally bounded energy. This includes the important example of vortex sheets, which exhibits the classical Kelvin-Helmholtz instabi...

Numerical Simulation of Vortex Breakdown by the Vortex-Filament Method