FINITE-ELEMENT SOLUTION OF THE STREAMFUNCTION-VORTICITY EQUATIONS FOR INCOMPRESSIBLE 2-DIMENSIONAL FLOWS

The streamfunction-vorticity equations for incompressible two-dimensional flows are uncoupled and solved in sequence by the finite element method. The vorticity at no-slip boundaries is evaluated in the framework of the streamfunction equation. The resulting scheme achieves convergence, even for very high values of the Reynolds number, without the traditional need for upwinding. The stability and accuracy of the approach are demonstrated by the solution of two well-known benchmark problems: flow in a lid-driven cavity at Re less than or equal to 10,000 and flow over a backward-facing step at Re = 800.