Table of Contents
ISRN Applied Mathematics
Volume 2012 (2012), Article ID 871538, 17 pages
http://dx.doi.org/10.5402/2012/871538
Research Article

Numerical Implementations for 2D Lid-Driven Cavity Flow in Stream Function Formulation

1Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
2Centre of Excellence in Mathematics, CHE, Si Ayutthaya Rd., Bangkok 10400, Thailand

Received 25 July 2012; Accepted 31 August 2012

Academic Editors: M.-H. Hsu, M. Langthjem, and M. Mei

Copyright © 2012 K. Poochinapan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The aim of this paper is to study the properties of approximations to nonlinear terms of the 2D incompressible Navier-Stokes equations in the stream function formulation (time-dependent biharmonic equation). The nonlinear convective terms are numerically solved by using the method with internal iterations, compared to the ones which are solved by using explicit and implicit schemes (operator splitting scheme Christov and Marinova; (2001)). Using schemes and algorithms, the steady 2D incompressible flow in a lid-driven cavity is solved up to Reynolds number Re with second-order spatial accuracy. The schemes are thoroughly validated on grids with different resolutions. The result of numerical experiments shows that the finite difference scheme with internal iterations on nonlinearity is more efficient for the high Reynolds number.