Methods of Solution of the Velocity-Vorticity Formulation of the Navier-Stokes Equations

Some methods are proposed for solving the Navier-Stokes equations for two-dimensional, incompressible, flow using the velocity-vorticity formulation. The main feature of the work is the solution of the equation of continuity using boundary-value techniques. This is possible because both of the velocity components are known at each boundary point. Some illustrative results are computed including some for heat convection inside a square cavity when one side is held at a constant temperature.