On upwind methods for parabolic finite elements in incompressible flows

We study the performance of various upwind techniques implemented in parabolic finite element discretizations for incompressible high Reynolds number flow. The characteristics of an ‘ideal’ upwind procedure are first discussed. Then the streamline upwind Petrov/Galerkin method, a simplified version thereof, the Galerkin least squares technique and a high-order derivative artificial diffusion method are evaluated on test problems. We conclude that none of the methods displays the desired solution characteristics. There is still need for the development of a reliable and efficient upwind method with characteristics close to those of the ‘ideal’ procedure.