PETROV-GALERKIN FINITE ELEMENT METHOD USING EXPONENTIAL FUNCTIONS FOR UNSTEADY INCOMPRESSIBLE VISCOUS FLOW PROBLEMS

Abstract

A new finite element scheme is proposed to solve numerically incompressible viscous flow problems for high Reynolds number governed by the unsteady Navier-Stokes equations. This scheme serves in the finite element formulation based on the Petrov-Galerkin method using exponential weighting function. The unsteady incompressible Navier-Stokes equations are discretized by the semi-explicit scheme with respect to a time variable. As the computational scheme, the fractional step method which is one of the time splitting techniques is used effectively in this study. The validity of the proposed method is shown by numerical solutions of several flow problems.