THE ANALYSIS OF UNSTEADY INCOMPRESSIBLE FLOWS BY A 3-STEP FINITE-ELEMENT METHOD

This paper describes a three-step finite element method and its applic ations to unsteady incompressible fluid flows. Stability analysis of t he one-dimensional pure convection equation shows that this method has third-order accuracy and an extended numerical stability domain in co mparison with the Lax-Wendroff finite element method. The method is co st-effective for incompressible flows because it permits less frequent updates of the pressure field with good accuracy. In contrast with th e Taylor-Galerkin method, the present method does not contain any new higher-order derivatives, which makes it suitable for solving non-line ar multidimensional problems and flows with complicated boundary condi tions. The three-step finite element method has been used to simulate unsteady incompressible flows. The numerical results obtained are in g ood agreement with those in the literature.