Chen, Ching-Jen; Chen, Hamn-Ching Finite analytic numerical method for unsteady two-dimensional Navier- Stokes equations. (English) Zbl 0546.76042 J. Comput. Phys. 53, 209-226 (1984). 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. Cited in 22 Documents MSC: 76D05 Navier-Stokes equations for incompressible viscous fluids 76M99 Basic methods in fluid mechanics Keywords:finite analytic (FA) numerical solution; unsteady two dimensional; small local element; starting cavity flow; vortex shedding flow behind a rectangular block PDFBibTeX XMLCite \textit{C.-J. Chen} and \textit{H.-C. Chen}, J. Comput. Phys. 53, 209--226 (1984; Zbl 0546.76042) Full Text: DOI References: [1] Chen, C. J.; Li, P., Finite differential method in heat conduction—Application of analytic solution technique, (ASME Paper, 79-WA/HT-50, December 2-7, ASME Winter Annual Meeting (1979)), 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., 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, (The 7th International Heat Transfer Conference. The 7th International Heat Transfer Conference, Munich (September 6-10, 1982)), 82-IHTC-43 [5] Roache, P. J., Computational Fluid Dynamics (1972), Hermosa Pub: 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: 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., (Finite Elements in Fluids, Vol. 3 (1978), Wiley: Wiley New York), 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: 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: 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. 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.