CONVERGENCE OF THE VARIABLE-ELLIPTIC-VORTEX METHOD FOR EULER EQUATIONS

A general formulation of the variable-elliptic-vortex method for the i ncompressible Euler equations is derived, and its consistency, stabili ty and convergence are proved. The main feature of this method is that not only the centers of the vortex blobs are transported by the induc ed velocity field, but also the blobs themselves are rotated and defor med in the elliptic shape according to the Jacobian matrix of the indu ced velocity field. The variable-elliptic-vortex method provides a mor e flexible and more reasonable approach to mimic physical Bows and all ows a smooth transition from vortex blobs to sheets and vice versa. Th e theoretic analysis indicates that the discretization error using var iable blobs is smaller than that using fixed blobs. Several issues on the practical aspects of the method are also addressed.