The Taylor vortex and the driven cavity problems by the stream function-vorticity formulation

We present here the Navier-Stokes equations using the stream function-vorticity formulation. In order to solve these equations we have used a simple numerical method based on a fixed point iterative process (1) to solve a nonlinear elliptic system resulting after time discretization. For this kind of problems efficient solvers like Fishpack (2) may be used. Results are presented for two problems: the Taylor vortex problem and the driven cavity problem. We present results, for the driven cavity problem for Reynolds numbers Re=3200 and Re=7500, and for the Taylor vortex problem with the same Reynolds numbers. With respect to the driven cavity problem, results agree very well with those reported in the literature (4 - 7). For the Taylor vortex problem (3), since the exact solution is known, the relative error was calculated and results were very good. Results are compared with those obtained for the same problems with other formulations (3 - 8).