Convergence of the point vortex method for the 3D Euler equations
Abstract
Consistency, stability, and convergence of a point vortex approximation to the 3D incompressible Euler equations with smooth solutions. The 3D algorithm considered is similar to the corresponding 3D vortex are proved blob algorithm introduced by Beale and Majda; The discretization error is secondorder accurate. Then the method is stable in l sup p norm for the particle trajectories and in w sup 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 the convergence result is that the vortex filament method without smoothing also converges.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 November 1990
 Bibcode:
 1990STIN...9121479H
 Keywords:

 Algorithms;
 Computational Fluid Dynamics;
 Convergence;
 Euler Equations Of Motion;
 Vortex Filaments;
 Differential Equations;
 Incompressible Flow;
 Particle Trajectories;
 Vortices;
 Fluid Mechanics and Heat Transfer