Stabilized finite element formulation for incompressible flow on distorted meshes

Flow computations frequently require unfavourably meshes, as for example highly stretched elements in regions of boundary layers or distorted elements in deforming arbitrary Lagrangian Eulerian meshes. Thus, the performance of a flow solver on such meshes is of great interest. The behaviour of finite elements with residual-based stabilization for incompressible Newtonian flow on distorted meshes is considered here. We investigate the influence of the stabilization terms on the results obtained on distorted meshes by a number of numerical studies. The effect of different element length definitions within the elemental stabilization parameter is considered. Further, different variants of residual-based stabilization are compared indicating that dropping the second derivatives from the stabilization operator, i.e. using a streamline upwind Petrov-Galerkin type of formulation yields better results in a variety of cases. A comparison of the performance of linear and quadratic elements reveals further that the inconsistency of linear elements equipped with residual-based stabilization introduces significant errors on distorted meshes, while quadratic elements are almost unaffected by moderate mesh distortion. Copyright (C) 2008 John Wiley & Sons, Ltd.