G. Comini et al., FINITE-ELEMENT SOLUTION OF THE STREAMFUNCTION-VORTICITY EQUATIONS FORINCOMPRESSIBLE 2-DIMENSIONAL FLOWS, International journal for numerical methods in fluids, 19(6), 1994, pp. 513-525
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.