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

Abstract

Paper presented to the 10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Florida, 14-16 July 2014.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].