Incompressible flow computations based on the vorticity-stream function and velocity-pressure formulations

Abstract

Finite element procedures and computations based on the velocity-pressure and vorticitystream function formulations of incompressible flows are presented. Two new multi-step velocity-pressure formulations are proposed and are compared with the vorticity-stream function and one-step formulations. The example problems chosen are the standing vortex problem and flow past a circular cylinder. Benchmark quality computations are performed for the cylinder problem. The numerical results indicate that the vorticity-stream function formulation and one of the two new multi-step formulations involve much less numerical dissipation than the one-step formulation.