×

Solutions of the two-dimensional Navier-Stokes equations by Chebyshev expansion methods. (English) Zbl 0587.76035

The steady two-dimensional Navier-Stokes equations in both the vorticity- stream function and the vorticity-velocity formulation are solved by Chebyshev expansion methods. Numerical experiments for the driven flow in a rectangular cavity and the developing flow in a circular tube at low Reynolds numbers are described.

MSC:

76Bxx Incompressible inviscid fluids
35Q30 Navier-Stokes equations
76M99 Basic methods in fluid mechanics
Full Text: DOI

References:

[1] Gatski, T. B.; Grosch, C. E.; Rose, M. E., A numerical study of the two-dimensional Navier-Stokes equations in vorticity-velocity variables, J. Comp. Phys., 48, 1-22 (1982) · Zbl 0502.76040
[2] Peyret, R.; Taylor, T. D., Computational Methods for Fluid Flow (1982), Springer-Verlag: Springer-Verlag New York
[3] Orszag, S. A., Spectral methods for problems in complex geometrics, J. Comp. Phys., 37, 70-92 (1980) · Zbl 0476.65078
[4] Y. Morchoisne, Pseudo-spectral space-time calculations of incompressible viscous flows. AIAA paper 81-0109, January 1981.; Y. Morchoisne, Pseudo-spectral space-time calculations of incompressible viscous flows. AIAA paper 81-0109, January 1981.
[5] Fox, L.; Parker, I. B., Chebyshev Polynomials in Numerical Analysis (1968), Oxford University Press: Oxford University Press London · Zbl 0153.17502
[6] Burggraf, O. R., Analytical and numerical studies of the structure of steady separated flows, J. Fluid Mech., 24, 113-151 (1966)
[7] Hirsh, R. S., Higher order accurate difference solutions of fluid mechanics problems by a compact differencing technique, J. Comp. Phys., 19, 90-109 (1975) · Zbl 0326.76024
[8] Langhaar, H. L., Steady flow in the transition length of a straight tube, Trans. ASME, 64, A55-A58 (1942)
[9] Hornbeck, R. W., Laminar flow in the entrance region of a pipe, Appl. Sci. Res., A13, 224-232 (1964) · Zbl 0125.17301
[10] Hatziavramidis, D. T.; Ku, H.-C., Pseudospectral solutions of laminar heat transfer problems in pipelines, J. Comp. Phys., 52, 414-424 (1983) · Zbl 0517.76007
[11] H.-C. Ku and D.T. Hatziavramidis, Chebyshev expansion methods for the solution of the extended Graetz problem. J. Comp. Phys.; H.-C. Ku and D.T. Hatziavramidis, Chebyshev expansion methods for the solution of the extended Graetz problem. J. Comp. Phys. · Zbl 0572.76084
[12] Ghia, K. N.; Hankey, W. L.; Hodge, J. K., A study of incompressible Navier-Stokes equations in primitive variables using an implicit numerical technique, AIAA paper 77-648 (1977)
[13] Van Dyke, M., Entry flow in a channel, J. Fluid Mech., 44, 813-823 (1970) · Zbl 0205.57001
[14] McDonald, J. W.; Denny, V. E.; Mills, A. F., Numerical solutions of the Navier-Stokes equations in inlet regions, J. Appl. Mech., 39, 873-878 (1972) · Zbl 0248.76009
[15] Vrentas, J. S.; Duda, J. L.; Bargeron, K. G., Effect of axial diffusion of vorticity on flow development in circular conduits: Part I. Numerical solutions, AIChE J., 12, 837-844 (1966)
[16] Hatziavramidis, D. T.; Ku, H.-C., Pseudospectral solutions of laminar heat transfer problems, (Proceedings 21st National Heat Transfer Conference. Proceedings 21st National Heat Transfer Conference, Seattle (1983)) · Zbl 0517.76007
[17] Fasel, H., Numerical solution of the unsteady Navier-Stokes equations for the investigation of laminar boundary layer stability, (Lecture Notes in Math., 771 (1980), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0356.76038
[18] Schreiber, R.; Keller, H. B., Driven cavity flows by efficient numerical techniques, J. Comp. Phys., 49, 310-333 (1983) · Zbl 0503.76040
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.