Direct numerical simulation of the flow in a lid-driven cubical cavity has been carried out at high Reynolds numbers (based on the maximum velocity on the lid), between 1.2 104 and 2.2 104. An efficient Chebyshev spectral method has been implemented for the solution of the incompressible Navier–Stokes equations in a cubical domain. The Projection-Diffusion method [Leriche and Labrosse (2000, SIAM J. Sci. Comput. 22(4), 1386–1410), Leriche et al. (2005, J. Sci. Comput., in press)] allows to decouple the velocity and pressure computation in very efficient way and the simple geometry allows to use the fast diagonalisation method for inverting the elliptic operators at a low computational cost. The resolution used up to 5.0 million Chebyshev collocation nodes, which enable the detailed representation of all dynamically significant scales of motion. The mean and root-mean-square velocity statistics are briefly presented
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Azaiez M., Bernardi C., and Grundmann M. (1995). Spectral method applied to porous media equations. East-West J. Numer. Math. 2:91–105
Batoul A., Khallouf H., and Labrosse G. (1994). Une méthode de résolution directe (Pseudo-Spectrale) du problème de Stokes 2D/3D instationnaire. Application à la Cavité Entrainée Carrée. C.R. Acad. Sci. Paris. 319(I):1455–1461
Bouffanais, R., Deville, M. O., Fischer, P. F., Leriche, E., and Weill, D. (2005). Direct and large eddy simulation of incompressible viscous fluid flow by the spectral element method. J. Sci. Comput. DOI: 10.1007/s10915-005-9039-7.
Canuto C., Hussaini M.Y., Quarteroni A., and Zang T.A. (1988). Spectral Methods in Fluid Dynamics. Springer Series in Computational Physics, Springer-Verlag, New-York
Deville M.O., Fischer P.F., and Mund E.H. (2002). High-Order Method for Incompressible Fluid Flow. Cambridge University Press, Cambridge
Gottlieb D., and Orszag S.A. (1977). Numerical Analysis of Spectral Methods: Theory and Applications. SIAM-CBMS, Philadelphia
Haldenwang P., Labrosse G., Abboudi S.A., and Deville M. (1984). Chebyshev 3D spectral and 2D pseudospectral solvers for the helmholtz equation. J. Comput. Phys. 55:115–128
Karniadakis G.E.M., Israeli M., and Orszag S.A. (1991). High-order splitting methods for the incompressible Navier–Stokes equations. J. Comput. Phys. 97:414–443
Karniadakis G.Em., and Sherwin S.J. (1999). Spectral/hp element methods for CFD. Oxford University Press, New-York
Labrosse G. (1993). Compatibility conditions for the Stokes system discretized in 2D cartesian domains. Comput. Meth. Appl. Mech. Eng. 106:353–365
Leriche, E. (1999). Direct Numerical Simulation of a Lid-Driven Cavity Flow by a Chebyshev Spectral Method. Ph.D thesis, no:1932, Ecole Polytechnique Fédérale de Lausanne, Lausanne
Leriche E., and Gavrilakis S. (2000). Direct numerical simulation of the flow in a lid-driven cubical cavity. Phys. Fluids 12(6):1363–1376
Leriche E., and Labrosse G. (2000). High-order direct Stokes solvers with or without temporal splitting: Numerical investigations of their comparative properties. SIAM J. Sci. Comput. 22(4):1386–1410
Leriche, E., Perchat, E., Labrosse, G., and Deville, M. O. (2005). Numerical evaluation of the accuracy and stability properties of high-order direct Stokes solvers with or without temporal splitting. To appear in J. Sci. Comput.
Lynch R.E., Rice J.R., and Thomas D.H. (1964). Direct solution of partial difference equations by tensor product methods. Numerishe Mathematik 6:185–199
Prasad A.K., and Koseff J.R. (1989). Reynolds number and end-wall effects on a lid-driven cavity flow. Phys. Fluids 1(2):208–218
Schumack M., Schultz W., and Boyd J. (1991). Spectral method solution of the Stokes equations on nonstaggered grids. J. Comput. Phys. 94:30–58
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Leriche, E. Direct Numerical Simulation in a Lid-Driven Cubical Cavity at High Reynolds Number by a Chebyshev Spectral Method. J Sci Comput 27, 335–345 (2006). https://doi.org/10.1007/s10915-005-9032-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10915-005-9032-1