A ψ–ω finite element formulations for the Navier‐Stokes equations

A new method of solving the two‐dimensional Navier–Stokes equations by using the finite element method is proposed. The flow is represented by the stream function–vorticity formulation and the no‐slip boundary conditions are explicitly introduced in the nonlinear equations. This formulation coupled with the Newton‐Raphson method enables the study of stationary flows for high Reynolds number, without any convergence problem. A number of flow problems are analysed in order to demonstrate the efficiency of the present formulation.