Discussion of numerical deficiency of applying a partially weighted upwind finite-element model to incompressible Navier-Stokes equations

The streamline upwind technique is extended to quadratic elements to analyze incompressible and viscous flow equations cast in the steady state. The Biased part of the weighting functions is devised to achieve a nodally exact discretized one-dimensional equation, with an emphasis on grid nonuniformity. Two classes of upwinding finite-element models are considered. Our primary goal is to address the deficiency of the partially weighted finite-element model. Assessment is made of the stability and accuracy of the schemes devised. The integrity of the weighting functions chosen and the finite-element models considered is demonstrated analytically, and their performance is assessed systematically.