Effect of boundary vorticity discretisation on explicit stream-function vorticity calculations

Abstract

The numerical solution of the time dependent Navier-Stokes equations in terms of the vorticity and a stream function is a well tested process to describe two-dimensional incompressible flows, both for fluid mixing applications and for studies in theoretical fluid mechanics. In this paper, we consider the interaction between the unsteady advection-diffusion equation for the vorticity, the Poisson equation linking vorticity and stream function and the approximation of the boundary vorticity, examining from a practical viewpoint, global error and iteration stability. Our results show that most schemes have very similar global stability constraints although there may be small stability gains from the choice of method to determine boundary vorticity