Title: Convergence study of the Chorin-Marsden formula

Speaker: Professor Longan Ying, Peking University and Penn State University

Date and place: Friday Apr. 14 3:30pm at UNIV 101

abstract.

The vortex method is applied to simulating viscous flow
numerically. The advantage of the vorticity-stream function
formulation is that it provides the motion of vorteces directly and it
is one approach for high-Reynold's number flow. The difficulty of the
vorticity-stream function formulation is that there is no a local
vorticity boundary condition. A "vorticity creation operator" is
introduced in the Chorin-Marsden formula to replace the boundary
condition. In this talk, We will present our study on the convergence
problem of the Chorin-Marsden formula for bounded domains. We first
consider the exact solution and introduce an integral equation with
Volterra type for the density of the vortex sheet, then we prove the
convergence of the approximate solutions. The order of convergence is
estimated, which is belived to be optimal. An comparison is made for
different kinds of approximate vortex sheets.