Convergence of a variable blob vortex method for the Euler and Navier-Stokes equations

Convergence is proved of the variable blob vortex method proposed [T. Hou, D. Papageorgiou, G. Papanicolaou, and J. Zhu, An adaptive vortex method for two-dimensional, viscous, and incompressible flows, preprint] for the incompressible Euler and Navier–Stokes equations without boundaries. This version of the variable blob method is designed to approximate directly the Navier–Stokes equations without matching the interior flow to the boundary layer solution. By choosing vortex blobs adaptively, the numerical errors due to local shear are minimized.