Direct numerical simulation in a lid-driven cubical cavity at high Reynolds number by a Chebyshev spectral method. (English) Zbl 1115.76379
Summary: 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 \(1.2\times 10^4\) and \(2.2\times 10^4\). 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 [E. Leriche and G. Labrosse [SIAM J. Sci. Comput. 22, No. 4, 1386–1410 (2000; Zbl 0972.35087), E. Leriche et al., J. Sci. Comput. 26, No. 1, 25–43 (2006; Zbl 1141.76047)] 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
MSC:
| 76M22 | Spectral methods applied to problems in fluid mechanics |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 76F65 | Direct numerical and large eddy simulation of turbulence |
References:
| [1] | Azaiez, M.; Bernardi, C.; Grundmann, M., Spectral method applied to porous media equations, East-West J. Numer. Math., 2, 91-105 (1995) · Zbl 0838.76055 |
| [2] | Batoul, A.; Khallouf, H.; Labrosse, G., 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 (1994) · Zbl 0816.76062 |
| [3] | 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. · Zbl 1099.76026 |
| [4] | Canuto, C.; Hussaini, M. Y.; Quarteroni, A.; Zang, T. A., Spectral Methods in Fluid Dynamics (1988), New-York: Springer-Verlag, New-York · Zbl 0658.76001 |
| [5] | Deville, M. O.; Fischer, P. F.; Mund, E. H., High-Order Method for Incompressible Fluid Flow (2002), Cambridge: Cambridge University Press, Cambridge · Zbl 1007.76001 |
| [6] | Gottlieb, D.; Orszag, S. A., Numerical Analysis of Spectral Methods: Theory and Applications (1977), Philadelphia: SIAM-CBMS, Philadelphia · Zbl 0412.65058 |
| [7] | Haldenwang, P.; Labrosse, G.; Abboudi, S. A.; Deville, M., Chebyshev 3D spectral and 2D pseudospectral solvers for the helmholtz equation, J. Comput. Phys., 55, 115-128 (1984) · Zbl 0544.65071 · doi:10.1016/0021-9991(84)90018-4 |
| [8] | Karniadakis, G. E.M.; Israeli, M.; Orszag, S. A., High-order splitting methods for the incompressible Navier-Stokes equations, J. Comput. Phys., 97, 414-443 (1991) · Zbl 0738.76050 · doi:10.1016/0021-9991(91)90007-8 |
| [9] | Karniadakis, G. Em.; Sherwin, S. J., Spectral/hp element methods for CFD (1999), New-York: Oxford University Press, New-York · Zbl 0954.76001 |
| [10] | Labrosse, G., Compatibility conditions for the Stokes system discretized in 2D cartesian domains, Comput. Meth. Appl. Mech. Eng., 106, 353-365 (1993) · Zbl 0783.76081 · doi:10.1016/0045-7825(93)90094-E |
| [11] | Leriche, E., Direct Numerical Simulation of a Lid-Driven Cavity Flow by a Chebyshev Spectral Method (1999), Lausanne: Ecole Polytechnique Fédérale de Lausanne, Lausanne |
| [12] | Leriche, E.; Gavrilakis, S., Direct numerical simulation of the flow in a lid-driven cubical cavity, Phys. Fluids, 12, 6, 1363-1376 (2000) · Zbl 1149.76452 · doi:10.1063/1.870387 |
| [13] | Leriche, E.; Labrosse, G., High-order direct Stokes solvers with or without temporal splitting: Numerical investigations of their comparative properties, SIAM J. Sci. Comput., 22, 4, 1386-1410 (2000) · Zbl 0972.35087 · doi:10.1137/S1064827598349641 |
| [14] | 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. · Zbl 1141.76047 |
| [15] | Lynch, R. E.; Rice, J. R.; Thomas, D. H., Direct solution of partial difference equations by tensor product methods, Numerishe Mathematik, 6, 185-199 (1964) · Zbl 0126.12703 · doi:10.1007/BF01386067 |
| [16] | Prasad, A. K.; Koseff, J. R., Reynolds number and end-wall effects on a lid-driven cavity flow, Phys. Fluids, 1, 2, 208-218 (1989) · doi:10.1063/1.857491 |
| [17] | Schumack, M.; Schultz, W.; Boyd, J., Spectral method solution of the Stokes equations on nonstaggered grids, J. Comput. Phys., 94, 30-58 (1991) · Zbl 0721.76057 · doi:10.1016/0021-9991(91)90136-9 |
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