CONVERGENCE OF PARTICLE METHODS WITH RANDOM REZONING FOR THE 2-DIMENSIONAL EULER AND NAVIER-STOKES EQUATIONS

We prove the convergence of a vortex method for the two-dimensional Euler and Navier-Stokes equations when only weak solutions are available. The approximation uses random rezoning at each time step and the convergence is obtained provided the various discretization parameters are linked by some power laws. The techniques rely on compactness properties similar to those giving the existence of weak solutions.