A multigrid method for solving the Navier–Stokes/Boussinesq equations
Article first published online: 5 JAN 2007
Copyright © 2007 John Wiley & Sons, Ltd.
Communications in Numerical Methods in Engineering
Volume 24, Issue 8, pages 671–681, August 2008
How to Cite
Cheikh, N. B., Beya, B. B. and Lili, T. (2008), A multigrid method for solving the Navier–Stokes/Boussinesq equations. Commun. Numer. Meth. Engng., 24: 671–681. doi: 10.1002/cnm.980
- Issue published online: 17 JUL 2008
- Article first published online: 5 JAN 2007
- Manuscript Accepted: 30 NOV 2006
- Manuscript Revised: 1 NOV 2006
- Manuscript Received: 1 JUL 2006
- natural convection;
- projection method
The present work investigates the efficiency and the accuracy of a multigrid (MG) technique for solving the Navier–Stokes/Boussinesq equations. In order to improve convergence, an accelerated full multigrid (AFMG) method with the iterative red and black successive over-relaxation smoother (RBSOR) is utilized. The AFMG method consists in introducing an accelerated parameter Γ>0 in the standard full multigrid procedure (FMG). A well-known benchmark problem is used to demonstrate the effectiveness and the accuracy of the method. Solutions are compared with those of the literature and show excellent agreement. Results for Prandtl numbers Pr=12.5, 6.8, 0.71 and 0.025 are also presented in this paper. It is observed that the mean heat transfer rate is minimum for Pr=0.71 and maximum for Pr=0.025. Copyright © 2007 John Wiley & Sons, Ltd.