Homogenization and convergence of the vortex method for 2-D euler equations with oscillatory vorticity fields

The 2-D incompressible Euler equations with oscillatory vorticity fields are studied. A homogenization result for 2-D Euler equations in velocity-vorticity formulation is obtained and weak continuity of the equations is proved. Convergence of the vortex method is analyzed in the case when the continuous vorticity is not well resolved by the computational particles. Numerical results are given. Comparisons are made with the corresponding finite difference approximation.