CONVERGENCE OF VORTEX METHODS FOR WEAK SOLUTIONS TO THE 2-D EULER EQUATIONS WITH VORTEX SHEET DATA

We prove the convergence of vortex blob methods to classical weak solu tions for the two-dimensional incompressible Euler equations with init ial data satisfying the conditions that the vorticity is a finite Rado n measure of distinguished sign and the kinetic energy is locally boun ded. This includes the important example of vortex sheets. The result is valid as long as the computational grid size h does not exceed the smoothing blob size epsilon, i.e., h/epsilon less than or equal to C. (C) 1995 John Wiley and Sons, Inc.