×

Finite analytic numerical method for unsteady two-dimensional Navier- Stokes equations. (English) Zbl 0546.76042

The main purpose of this paper is to develop a finite analytic (FA) numerical solution for unsteady two dimensional Navier-Stokes equations. The FA method utilizes the analytic solution in a small local element to formulate the algebraic representation of partial differential equations. In this study the combination of linear and exponential functions that satisfy the governing equation is adopted as the boundary function, thereby improving the accuracy of the finite analytic solution. Two flows, one a starting cavity flow and the other a vortex shedding flow behind a rectangular block, are solved by the FA method.

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
76M99 Basic methods in fluid mechanics
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Chen, C.J.; Li, P., Finite differential method in heat conduction—application of analytic solution technique, (), New York
[2] Chen, C.J.; Li, P., The finite analytic method for steady and unsteady heat transfer problems, ASME paper, 80-HT-86, (1980)
[3] Chen, C.J.; Nasert-Neshat, H.; Ho, K.S.; Chen, C.J.; Nasert-Neshat, H.; Ho, K.S., Finite analytic numerical solution of heat transfer in two-dimensional cavity flow, (), J. numer. heat transfer, 4, 179, (1981)
[4] Chen, C.J.; Obasih, K., Finite analytic numerical solution of heat transfer and flow past a square channel cavity, (), 82-IHTC-43
[5] Roache, P.J., Computational fluid dynamics, (1972), Hermosa Pub Albuquerqe, N. Mex · Zbl 0251.76002
[6] Spalding, D.B., Int. numer. methods eng., Vol 4, 551, (1972)
[7] Patankar, S.V., Numerical heat transfer and fluid flow, (1980), McGraw-Hill New York · Zbl 0595.76001
[8] Heinrich, J.C.; Huyakorn, P.S.; Zienkiewiez, O.C.; Mitchell, A.R., Int. J. numer. methods eng., 11, 131, (1977)
[9] Gallagher, R.H.; Oden, J.T.; Taylor, C.; Zienkiewiez, O.C., (), 1
[10] Dennis, S.C.R.; Hudson, J.D., J. inst. math. its appl., 26, 369, (1980)
[11] Barrett, K.E.; Demunski, G., Int. J. numer. methods eng., 14, 1511, (1979)
[12] Shay, W.A., Comput. fluids, 9, 279, (1981)
[13] Gosman, A.D.; Pun, W.M.; Runchal, A.K.; Spalding, D.B., Heat and mass transfer in recirculating flows, (1969), Academic Press New York/London · Zbl 0239.76001
[14] Rubin, S.G.; Khosla, P.K., J. comput. phys., 24, 217, (1977)
[15] Nallasamy, M.; Prasad, K.K., J. fluid mech., 79, 2, 391, (1977)
[16] Quartapelle, L., J. comput. phys., 40, 453, (1981)
[17] Pan, F.; Acrivos, A., J. fluid mech., 28, 4, 653, (1967)
[18] Blevins, R.D., Flow-induced vibration, (1977), Van Nostrand-Reinhold Princeton, N. J, Chap. 1 · Zbl 0385.73001
[19] Fromm, J.E.; Harlow, F.H., Phys. fluids, 6, 7, 975, (1963)
[20] Smith, S.L.; Brebbias, C.A., J. comput. phys., 17, 235, (1975)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.