Simulation of Viscous Diffusion for Extension of the Surface Vorticity Method to Boundary Layer and Separated Flows

A numerical method for two-dimensional incompressible viscous fluid flows is tested on the diffusion of a point vortex. It is then applied to the boundary layer to reconstruct the Blasius profile, to demonstrate flow separation, and to simulate turbulence. The significance of Thwaites' boundary layer parameter for flow separation is explained. The Kelvin-Helmholtz instability, which is responsible for two-dimensional turbulence, is represented by the motion of an array of point vortices after an initial disturbance. The formation of the Von Karman vortex street downstream of a circular cylinder is described by computer simulation, and the influence of viscous diffusion is shown. For two different cylinder Reynolds numbers the vortex shedding frequencies and oscillating lift and drag forces are evaluated.