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.

Linked References

  1. C. I. Christov and R. S. Marinova, “Implicit vectorial operator splitting for incompressible Navier-Stokes equations in primitive variables,” Computational Technologies, vol. 6, no. 4, pp. 92–119, 2001. View at Google Scholar · View at Zentralblatt MATH
  2. S. Abdallah, “Numerical solutions for the incompressible Navier-Stokes equations in primitive variables using a non-staggered grid, II,” Journal of Computational Physics, vol. 70, no. 1, pp. 193–202, 1987. View at Google Scholar · View at Scopus
  3. C. H. Bruneau and C. Jouron, “An efficient scheme for solving steady incompressible Navier-Stokes equations,” Journal of Computational Physics, vol. 89, no. 2, pp. 389–413, 1990. View at Publisher · View at Google Scholar · View at Scopus
  4. C. H. Bruneau and M. Saad, “The 2D lid-driven cavity problem revisited,” Computers and Fluids, vol. 35, no. 3, pp. 326–348, 2006. View at Publisher · View at Google Scholar · View at Scopus
  5. U. Ghia, K. N. Ghia, and C. T. Shin, “High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method,” Journal of Computational Physics, vol. 48, no. 3, pp. 387–411, 1982. View at Google Scholar · View at Scopus
  6. S. Smagulov and C. I. Christov, “Iterationless numerical implementation of the boundary conditions in vorticity-stream function formulation of Navier-Stokes equations,” Institute of Theoretical and Applied Mechanics, Russian Academy of Science, Novosibirsk, Russia, 1980.
  7. P. N. Vabishchevich, “Implicit finite-difference schemes for the nonstationary Navier-Stokes equations with the stream function and vorticity as variables,” Differential Equations, vol. 20, pp. 820–827, 1984. View at Google Scholar
  8. M. Napolitano, G. Pascazio, and L. Quartapelle, “A review of vorticity conditions in the numerical solution of the ζ-ψ equations,” Computers & Fluids, vol. 28, no. 2, pp. 139–185, 1999. View at Publisher · View at Google Scholar
  9. M. Li, T. Tang, and B. Fornberg, “A compact fourth-order finite difference scheme for the steady incompressible Navier-Stokes equations,” International Journal for Numerical Methods in Fluids, vol. 20, no. 10, pp. 1137–1151, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. C. I. Christov and A. Ridha, “Splitting scheme for iterative solution of bi-harmonic equation, Application to 2D Navier-Stokes problems,” Advances in Numerical Methods and Applications, pp. 341–352, 1994. View at Google Scholar
  11. C. I. Christov and A. Ridha, “Splitting scheme for the stream-function formulation of 2D unsteady Navier-Stokes equations,” Comptes Rendus Academie des Sciences, Serie II, vol. 320, no. 9, pp. 441–446, 1995. View at Google Scholar · View at Scopus
  12. G. I. Marchuk, Methods of Numerical Mathematics, Springer, New York, NY, USA, 1975.
  13. C. I. Christov and X.-H. Tang, “An operator splitting scheme for the stream-function formulation of unsteady Navier-Stokes equations,” International Journal for Numerical Methods in Fluids, vol. 53, no. 3, pp. 417–442, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. O. Botella and R. Peyret, “Benchmark spectral results on the lid-driven cavity flow,” Computers and Fluids, vol. 27, no. 4, pp. 421–433, 1998. View at Publisher · View at Google Scholar · View at Scopus
  15. W. F. Spotz, “Accuracy and performance of numerical wall boundary conditions for steady, 2D, incompressible streamfunction vorticity,” International Journal for Numerical Methods in Fluids, vol. 28, no. 4, pp. 737–757, 1998. View at Google Scholar