A semi-analytic method for the evolution of closed vortex sheets (Q1339405)

A new semi-analytical method for following the evolution of closed vortex sheets is presented. The governing integro-differential equation for vortex sheet motion is reduced to a set of partial differential equations, using complex analysis together with the famous Riemann mapping theorem. These equations are solved by a simple finite difference scheme. The method is used to study numerically the evolution of initially elliptic vortex sheet. To start the new method, the initial shape and intensity of vorticity distribution should be represented by trigonometric series.