Document Type: Research Paper


1 Ph.D candidate, Hydraulic division, Middle East Technical University

2 Hydraulic division, Middle East Technical University, Ankara,

3 Department of Water Engineering, University of Zanjan, Zanjan, Iran


In this study, a numerical solution of 2D steady incompressible lid-driven cavity flow is presented. Three different numerical schemes were employed to make a comparison on the practicality of the methods. An alternating direction implicit scheme for the vorticity-stream function formulation, explicit and implicit schemes for the primitive variable formulation of governing Navier-Stokes equations were attempted. A fairly fine uniform grid was adopted for all the cases after a technical procedure was applied to come up with the proper mesh size that would make the solution roughly independent of mesh quality. The solutions obtained for different Reynolds numbers are presented and compared. Superiority of numerical approaches was investigated and compared to benchmark solutions available in the literature. Based on the results of the present research, it can be claimed that explicit scheme used for primitive variable formulation can be only half the way (as in Re=2500 for explicit to Re=5000 for ADI and implicit schemes) as successful as the other two numerical methods due to its relative simplicity.

Graphical Abstract


Main Subjects

[1]          E. Erturk, “Discussions on Driven Cavity Flow”, International Journal for Numerical Methods in Fluids, Vol. 60, No. 3, pp. 275-294, (2009).

[2]          M. S. Chandio, M. U. Jhatila, and S. F. Shan, “Finite Element Simulation of Newtonian Lid-Driven Cavity Flow”, Research Journal, Vol. 45, No. 2, pp. 253-262, (2013).

[3]        K. Gustafson, “Four principles of vortex motion”, Vortex Methods and Vortex Motion, Eds. K. Gustafson and J. Sethian, SIAM Publications, Philadelphia, pp. 95-141, (1991).

[4]          Y. F. Peng, Y. H. Shiau, and R. R. Hwang “Transition in a 2-D Lid-Driven Cavity Flow”, Computers and Fluids, Vol. 32, No. 3, pp. 337-352, (2003).

[5]          C. H. Bruneau, and M. Saad, “The 2D Lid Driven Cavity Problem Revisited”, Computers and Fluids, Vol. 35, No. 3, pp. 326-348, (2006).

[6]          U. Ghia, K. N. Ghia, and C. T. Shin, “High-Re Solutions for Incompressible Flow Using the Navier-Stokes Equations and a Multi grid Method”, Journal of Computational Physics, Vol. 48, No. 3, pp. 387-411, (1982).

[7]          E. Barragy, and G. F. Carey, “Stream Function-Vorticity Driven Cavity Solutions Using P-Finite Elements”, Computers and Fluids, Vol. 26, No. 5, pp. 453-468, (1997).

[8]          P. S. B. Zdanski, M. A. Ortega, and N. G. C. R. Fico, “Numerical Study of the Flow Over Shallow Cavities”, Computers and Fluids, Vol. 32, No. 7, pp. 953-974, (2003).

[9]          D. S. Kumar, K. S. Kumar, and M. K. Das, “A Fine Grid Solution for a Lid-Driven Cavity Flow Using Multigrid Method”, Engineering Applications of Computational Fluid Mechanics, Vol. 3, No. 3, pp. 336-354, (2009).

[10]      N. P. Moshkin, and K. Poochinapan, “Novel finite difference scheme for the numerical solution of two-dimensional incompressible Navier-Stokes equations”, International Journal Of Numerical Analysis And Modeling, Vol. 7, No. 2, pp. 321-329, (2010).

[11]      K. Poochinapan, “Numerical implementations for 2-d lid-driven cavity flow in stream function formulation”, ISRN Applied Mathematics, Vol. 2012, Article ID: 871538, 17 pp, (2012).

[12]      K. Yapici, and Y. Uludag, “Finite volume simulation of 2-d steady square lid driven cavity flow at high Reynolds numbers”, Brazilian Journal of Chemical Engineering, Vol. 30, No. 4, pp. 923-937, (2013).

[13]      K. M. Salah Uddin, and L. K. Saha, “Numerical solution of 2-d incompressible   driven  cavity  flow  with

wavy bottom surface”, American Journal of Applied Mathematics, Vol. 3, No. 1-1, pp. 30-42, (2015).

[14]      L. Marioni, F. Bay, and E. Hachem, “Numerical stability analysis and flow simulation of lid-driven cavity subjected to high magnetic field”, Physics of Fluids, Vol. 28, Article ID 057102, 16 pp, (2016).

[15]      D. C. Wan, Y. C. Zhou, and G. W. Wei, “Numerical solution of incompressible flows by discrete singular convolution”, International Journal For Numerical Methods In Fluids, Vol. 38, No. 8, pp. 789-810, (2002).

[16]      B. E. Launder, and D. B. Spalding, “The Numerical Computation of Turbulent Flows”, Computer Methods in Applied Mechanics and Engineering, Vol. 3, No. 2, pp. 269-289, (1974).

[17]      E. Erturk, T. C. Corke, and C. Gokcol, “Numerical Solutions of 2-D Steady Incompressible Driven Cavity Flow at High Reynolds Numbers”, International Journal For Numerical Methods In Fluids,   Vol.  48,   No.  7,   pp.  747-774,


[18]      E. Erturk, and C. Gokcol, “Fourth Order Compact Formulation of Navier- Stokes Equations and Driven Cavity Flow at High Reynolds Numbers”, International Journal For Numerical Methods In Fluids, Vol. 50, No. 4, pp. 421-436, (2006).