A numerical study of the two-dimensional Navier-Stokes equations in vorticity-velocity variables

The application of solution methods for compact finite-difference schemes to a vorticity-velocity form of the two-dimensional unsteady Navier-Stokes equations is described. An account is also given of numerical experiments for stagnation point and driven cavity flows. One experiment treats the flow impinging on a flat plate, and the numerical results can be compared with the analytical steady state solution (Batchelor, 1967). The other deals with the driven cavity problem, the primary purpose being to describe the time evolution of this classical problem (Donovan, 1970).