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

The streamfunction-vorticity equations for incompressible two-dimensio nal flows are uncoupled and solved in sequence by the finite element m ethod. The vorticity at no-slip boundaries is evaluated in the framewo rk of the streamfunction equation. The resulting scheme achieves conve rgence, even for very high values of the Reynolds number, without the traditional need for upwinding. The stability and accuracy of the appr oach are demonstrated by the solution of two well-known benchmark prob lems: flow in a lid-driven cavity at Re less than or equal to 10,000 a nd flow over a backward-facing step at Re = 800.