×

Discussions on driven cavity flow. (English) Zbl 1162.76047

Summary: The widely studied benchmark problem, two-dimensional-driven cavity flow problem, is discussed in detail in terms of physical and mathematical and also numerical aspects. We give a very brief literature survey on studies on the driven cavity flow. On the basis of several numerical and experimental studies, the fact of the matter is that physically the flow in a driven cavity is not two-dimensional above moderate Reynolds numbers. However, there exist numerical solutions for two-dimensional-driven cavity flow at high Reynolds numbers.

MSC:

76M99 Basic methods in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Erturk, Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers, International Journal for Numerical Methods in Fluids 48 pp 747– (2005) · Zbl 1071.76038
[2] Erturk, Fourth order compact formulation of Navier-Stokes equations and driven cavity flow at high Reynolds numbers, International Journal for Numerical Methods in Fluids 50 pp 421– (2006) · Zbl 1086.76053
[3] Barragy, Stream function-vorticity driven cavity solutions using p finite elements, Computers and Fluids 26 pp 453– (1997) · Zbl 0898.76053
[4] Schreiber, Driven cavity flows by efficient numerical techniques, Journal of Computational Physics 49 pp 310– (1983) · Zbl 0503.76040
[5] Benjamin, On the convergence of numerical solutions for 2-D flows in a cavity at large Re, Journal of Computational Physics 33 pp 340– (1979) · Zbl 0421.76020
[6] Liao, A short note on higher-order streamfunction-vorticity formulation of 2-D steady state Navier-Stokes equations, International Journal for Numerical Methods in Fluids 22 pp 1– (1996)
[7] Ghia, High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, Journal of Computational Physics 48 pp 387– (1982) · Zbl 0511.76031
[8] Fortin, Localization of Hopf bifurcations in fluid flow problems, International Journal for Numerical Methods in Fluids 24 pp 1185– (1997) · Zbl 0886.76042
[9] Gervais, Some experiments with stability analysis of discrete incompressible flows in the lid-driven cavity, International Journal for Numerical Methods in Fluids 24 pp 477– (1997) · Zbl 0890.76037 · doi:10.1002/(SICI)1097-0363(19970315)24:5<477::AID-FLD500>3.0.CO;2-S
[10] Sahin, A novel fully-implicit finite volume method applied to the lid-driven cavity flow problem. Part II. Linear stability analysis, International Journal for Numerical Methods in Fluids 42 pp 79– (2003) · Zbl 1078.76047
[11] Abouhamza, A neutral stability curve for incompressible flows in a rectangular driven cavity, Mathematical and Computer Modelling 38 pp 141– (2003) · Zbl 1053.76019
[12] Auteri, Numerical investigation on the stability of singular driven cavity flow, Journal of Computational Physics 183 pp 1– (2002) · Zbl 1021.76040
[13] Peng, Transition in a 2-D lid-driven cavity flow, Computers and Fluids 32 pp 337– (2003)
[14] Tiesinga, Bifurcation analysis of incompressible flow in a driven cavity by the Newton-Picard method, Journal of Computational and Applied Mathematics 140 pp 751– (2002) · Zbl 1063.76040
[15] Poliashenko, A direct method for computation of simple bifurcations, Journal of Computational Physics 121 pp 246– (1995) · Zbl 0840.76076
[16] Cazemier, Proper orthogonal decomposition and low-dimensional models for the driven cavity flows, Physics of Fluids 10 pp 1685– (1998)
[17] Goyon, High-Reynolds number solutions of Navier-Stokes equations using incremental unknowns, Computer Methods in Applied Mechanics and Engineering 130 pp 319– (1996) · Zbl 0865.76050
[18] Wan, Numerical solution of incompressible flows by discrete singular convolution, International Journal for Numerical Methods in Fluids 38 pp 789– (2002) · Zbl 1005.76072
[19] Liffman, Comments on a collocation spectral solver for the Helmholtz equation, Journal of Computational Physics 128 pp 254– (1996) · Zbl 0859.65119
[20] Koseff, The lid-driven cavity flow: a synthesis of qualitative and quantitative observations, ASME Journal of Fluids Engineering 106 pp 390– (1984)
[21] Koseff, On end wall effects in a lid driven cavity flow, ASME Journal of Fluids Engineering 106 pp 385– (1984)
[22] Koseff, Visualization studies of a shear driven three-dimensional recirculating flow, ASME Journal of Fluids Engineering 106 pp 21– (1984)
[23] Prasad, Reynolds number and end-wall effects on a lid-driven cavity flow, Physics of Fluids A 1 pp 208– (1989)
[24] Weinan, Vorticity boundary condition and related issues for finite difference schemes, Journal of Computational Physics 124 pp 368– (1996) · Zbl 0847.76050
[25] Tannehill, Computational Fluid Mechanics and Heat Transfer (1997)
[26] Fletcher, Computational Techniques for Fluid Dynamics (1991) · Zbl 0717.76001 · doi:10.1007/978-3-642-58239-4
[27] Aydin, Boundary element analysis of driven cavity flow for low and moderate Reynolds numbers, International Journal for Numerical Methods in Fluids 37 pp 45– (2001) · Zbl 1017.76058
[28] Shankar, Fluid mechanics in the driven cavity, Annual Review of Fluid Mechanics 32 pp 93– (2000) · Zbl 0988.76006
[29] Kim, Application of a fractional-step method to incompressible Navier-Stokes equations, Journal of Computational Physics 59 pp 308– (1985) · Zbl 0582.76038
[30] Schlichting, Boundary Layer Theory (2000) · Zbl 0940.76003 · doi:10.1007/978-3-642-85829-1
[31] Drazin, Hydrodynamic Stability (1991)
[32] Haddad, Boundary layer receptivity to free-stream sound on parabolic bodies, Journal of Fluid Mechanics 368 pp 1– (1998) · Zbl 0927.76027
[33] Erturk, Boundary layer leading-edge receptivity to sound at incidence angles, Journal of Fluid Mechanics 444 pp 383– (2001) · Zbl 1039.76024
[34] Erturk, Numerical solutions of laminar incompressible flow past parabolic bodies at angles of attack, AIAA Journal 42 pp 2254– (2004)
[35] Ramanan, Linear stability of lid-driven cavity flow, Physics of Fluids 6 pp 2690– (1994) · Zbl 0837.76031
[36] Ding, Linear stability of incompressible fluid flow in a cavity using finite element method, International Journal for Numerical Methods in Fluids 27 pp 139– (1998) · Zbl 0909.76047
[37] Albensoeder, Three-dimensional centrifugal-flow instabilities in the lid-driven cavity problem, Physics of Fluids 13 pp 121– (2001) · Zbl 1184.76025
[38] Albensoeder, Accurate three-dimensional lid-driven cavity flow, Journal of Computational Physics 206 pp 536– (2005) · Zbl 1121.76366
[39] Smith, A structure for laminar flow past a bluff body at high Reynolds number, Journal of Fluid Mechanics 155 pp 175– (1985) · Zbl 0586.76054
[40] Peregrine, A note on the steady high-Reynolds-number flow about a circular cylinder, Journal of Fluid Mechanics 157 pp 493– (1985)
[41] Fornberg, A numerical study of steady viscous flow past a circular cylinder, Journal of Fluid Mechanics 98 pp 819– (1980) · Zbl 0428.76032
[42] Fornberg, Steady viscous flow past a circular cylinder up to Reynolds number 600, Journal of Computational Physics 61 pp 297– (1985) · Zbl 0576.76026
[43] Son, Numerical solution for the flow around a cylinder at Reynolds numbers of 40, 200 and 500, Journal of Fluid Mechanics 35 pp 369– (1969) · Zbl 0164.28202
[44] Tuann, Numerical studies of the flow around a circular cylinder by a finite element method, Computers and Fluids 6 pp 219– (1978) · Zbl 0394.76038
[45] Dennis, Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100, Journal of Fluid Mechanics 42 pp 471– (1970) · Zbl 0193.26202
[46] Burggraf, Analytical and numerical studies of the structure of steady separated flows, Journal of Fluid Mechanics 24 pp 113– (1966)
[47] Batchelor, On steady laminar flow with closed streamlines at large Reynolds numbers, Journal of Fluid Mechanics 1 pp 177– (1956) · Zbl 0070.42004
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.