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

摘要

A general formulation of the variable-elliptic-vortex method for the incompressible Euler equations is derived, and its consistency, stability and convergence are proved. The main feature of this method is that not only the centers of the vortex blobs are transported by the induced velocity field, but also the blobs themselves are rotated and deformed in the elliptic shape according to the Jacobian matrix of the induced velocity field. The variable-elliptic-vortex method provides a more flexible and more reasonable approach to mimic physical Bows and allows a smooth transition from vortex blobs to sheets and vice versa. The theoretic analysis indicates that the discretization error using variable blobs is smaller than that using fixed blobs. Several issues on the practical aspects of the method are also addressed. [References: 18]