Core spreading vortex methods in two-dimensional viscous flows Original Research Article

The purpose of the present paper is: (1) to derive an integral equation of Fredholm type with respect to vorticity from the two-dimensional Navier-Stokes equations, (2) to derive two vortex methods which are based on the core spreading model and (3) to analyze them, by using this integral equation. The convergence and stability properties of two methods, the Gaussian core spreading model and the alternative Gaussian core spreading model, for high Reynolds number flows are analyzed under the assumption of smooth initial condition with bounded support and a free-space boundary.