Finite Element Simulation of Newtonian Lid-Driven Cavity Flow

Abstract

In this paper we have proposed a numerical scheme for the solution of two dimensional, steady state isothermal and incompressible Navier-Stokes equations. The proposed method is the modified version of semi-implicit Taylor-Galerkin-PressureCorrection algorithm (Chandio and Webster 2002). The projection method, originally developed for unsteady flow problems by Chorin and Temam (1968), is used here for solving incompressible Navier-Stokes equations for the solution of primitive variables. The velocity and pressure fields are computed in a decoupled manner. To validate the accuracy and consistency of the proposed scheme, one-sided lid driven square cavity is considered here. The behaviour of primary, secondary and tertiary vortices are investigated at high Reynolds numbers. The governing equations are discretized using Galerkin finite element method. Simulation is performed for a various Reynolds numbers ranging from 500 to 20000. The obtained results are compared with the experimental and numerical results available in the literature and are in good agreement with them.