Numerical Simulation of 2D Square Driven Cavity
Using Fourth Order Compact Finite Difference Schemes

Jun Zhang
Department of Computer Science
University of Kentucky
773 Anderson Hall
Lexington, KY 40506-0046, USA

Abstract

Fourth order compact finite difference schemes are employed with multigrid techniques to simulate the two dimensional square driven cavity flow with small to large Reynolds numbers. The governing Navier-Stokes equation is linearized in streamfunction and vorticity formulation. The fourth order compact approximation schemes are coupled with fourth order approximations for velocities and vorticity boundaries. Numerical solutions are obtained for square driven cavity flow at high Reynolds numbers and are compared with solutions obtained by other researchers using other approximation methods.


Key words: Incompressible Navier-Stokes equations, square driven cavity problem, convection diffusion equation, multigrid method, fourth order compact discretization.


This paper has been published in Computers and Mathematics with Applications, Vol. 45, pp. 43-52, (2003).