Convergence of the Point Vortex Method for the 3-D Euler Equations

摘要

Consistency, stability, and convergence of a point vortex approximation to the 3-D incompressible Euler equations with smooth solutions. The 3-D algorithm considered here is similar to the corresponding 3-D vortex are proved blob algorithm introduced by Beale and Majda; The discretization error is second-order accurate. Then the method is stable in l superscript p norm for the particle trajectories and in w superscript -1,p norm for discrete vorticity. Consequently, the method converges up to any time for which the Euler equations have a smooth solution. One immediate application of our convergence result is that the vortex filament method without smoothing also converges.