Finite-element Navier-Stokes analysis of the flow about a finite plate

Abstract

The problem considered is the classical case of laminar flow about a finite flat plate over the range IO2 < Ret ^ IO5, treating the whole flow field with particular emphasis on the leading and trailing edges and the near wake. It was worthwhile to revisit this problem using modern numerical methods for the Navier-Stokes equations because it was found that the agreement between the existing predictions and newer experiments is surprisingly poor for some key features of the flow. The present work uses a weak Galerkin formulation for the finite-element method with the pressure determined by a penalty approach. The results are presented mainly in terms of the skin-friction coefficient on the plate, the wake centerline velocity variation, and the velocity variation along the upstream stagnation streamline. Thick plates are also considered. The results are compared to earlier analyses and experiments. Finally, the case of a three-dimensional finite width (L = W) flat plate at RCL = IO2 and IO3 is treated and discussed.