The solution to the problem of vortex breakdown

Abstract

A numerical solution of the Navier-Stokes equations is discussed for time-dependent, three-dimensional, incompressible flow. The solution is based on the artificial compressibility concept and a dual time stepping procedure. An implicit Roe-type flux-difference splitting is used for the discretization of the convective and central differencing for the viscous terms. The difference equations are written for a Cartesian grid. A new approximation for the downstream boundary conditions is derived. The solution was employed to describe the process of vortex breakdown in isolated slender vortices. It is shown, that stable breakdown can be achieved by iterating the side boundary conditons through a new integral technique. Comparison with experimental flow visualizations shows good qualitative agreement between the vortex structures observed in experiments and simulations.