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Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers. (English) Zbl 1071.76038
Summary: Numerical calculations of the 2-D steady incompressible driven cavity flow are presented. The Navier-Stokes equations in streamfunction and vorticity formulation are solved numerically using a fine uniform grid mesh of \(601 \times 601\). The steady driven cavity flow solutions are computed for \(\text{Re} \leqslant 21 000\) with a maximum absolute residuals of the governing equations that were less than \(10^{-10}\). A new quaternary vortex at the bottom left corner and a new tertiary vortex at the top left corner of the cavity are observed in the flow field as the Reynolds number increases. Detailed results are presented and comparisons are made with benchmark solutions found in the literature.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
76D17 Viscous vortex flows
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References:
[1] Aydin, International Journal for Numerical Methods in Fluids 37 pp 45– (2001)
[2] Barragy, Computers and Fluids 26 pp 453– (1997)
[3] Batchelor, Journal of Fluid Mechanics 1 pp 177– (1956)
[4] Beam, AIAA Journal 16 pp 393– (1978)
[5] Benjamin, Journal of Computational Physics 33 pp 340– (1979)
[6] Botella, Computers and Fluids 27 pp 421– (1998)
[7] Bruneau, Journal of Computational Physics 89 pp 389– (1990)
[8] Burggraf, Journal of Fluid Mechanics 24 pp 113– (1966)
[9] Erturk, Journal of Fluid Mechanics 444 pp 383– (2001)
[10] Erturk, AIAA Journal 42 pp 2254– (2004)
[11] Fortin, International Journal for Numerical Methods in Fluids 24 pp 1185– (1997)
[12] Ghia, Journal of Computational Physics 48 pp 387– (1982)
[13] Goyon, Computer Methods in Applied Mechanics and Engineering 130 pp 319– (1996)
[14] Grigoriev, International Journal for Numerical Methods in Engineering 46 pp 1127– (1999)
[15] Gupta, Journal of Computational Physics 93 pp 343– (1991)
[16] Gupta, Journal of Computational Physics 31 pp 265– (1979)
[17] Hou, Journal of Computational Physics 118 pp 329– (1995)
[18] Li, International Journal for Numerical Methods in Fluids 20 pp 1137– (1995)
[19] Liao, International Journal for Numerical Methods in Fluids 15 pp 595– (1992)
[20] Liao, International Journal for Numerical Methods in Fluids 22 pp 1– (1996)
[21] Nallasamy, Journal of Fluid Mechanics 79 pp 391– (1977)
[22] Nishida, International Journal for Numerical Methods in Fluids 34 pp 637– (1992) · Zbl 0757.76049
[23] Peng, Computers and Fluids 32 pp 337– (2003)
[24] Poliashenko, Journal of Computational Physics 121 pp 246– (1995) · Zbl 0887.65095
[25] Rubin, Computers and Fluids 9 pp 163– (1981)
[26] Schreiber, Journal of Computational Physics 49 pp 310– (1983)
[27] Shankar, Annual Review of Fluid Mechanics 32 pp 93– (2000)
[28] Spotz, International Journal for Numerical Methods in Fluids 28 pp 737– (1998)
[29] Computational Fluid Mechanics and Heat Transfer (2nd edn). Taylor & Francis: London, 1997.
[30] Thom, Proceedings of the Royal Society of London Series A 141 pp 651– (1933)
[31] Vanka, Journal of Computational Physics 65 pp 138– (1986) · Zbl 0604.76025
[32] Weinan, Journal of Computational Physics 124 pp 368– (1996)
[33] Wood, Journal of Fluid Mechanics 2 pp 77– (1957)
[34] Wright, Computers and Fluids 24 pp 63– (1995)
[35] Napolitano, Computers and Fluids 28 pp 139– (1999)
[36] Huang, Journal of Computational Physics 126 pp 468– (1996)
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.