A procedure is proposed for the integration of the full Navier-Stokes equations for constant-property two-dimensional flows. In contrast with earlier procedures, the present one is capable of dealing with cases of very high Reynolds number. The power of the new procedure is demonstrated in two cases: (1) the square recirculating eddy, for which no solution was previously available for Reynolds numbers larger than about 400, and (2) an impinging jet, for which no solution was available previously. The procedure has also been applied to the square cavity at Reynolds numbers below 400; it gives results of an accuracy comparable with that of previous solutions, but with a smaller computing time.
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References
1.
ThomA.‘The flow past circular cylinders at low speeds’, Proc. R. Soc.1933141, (Series A), 651.
2.
KawagutiM.‘Numerical solution of the Navier-Stokes equations for the flow around a circular cylinder at Reynolds number 40’, J. phys. Soc. Japan19538, (No. 6), 747.
3.
de AllenD. N. G.SouthwellR. V.‘Relaxation methods applied to determine the motion, in two dimensions, of a viscous fluid past a fixed cylinder’, Quart. J. Mech. appl. Math.19588, (No. 2), 129.
4.
RunchalA. K.WolfshteinM.‘A finite difference procedure for the integration of the Navier-Stokes equation’, Department of Mechanical Engineering, Imperial College, London, Ref. No. SN/TN/1, 1966.
5.
ThomA.ApeltC. J.Field computation in engineering and physics1961 (D. van Nostrand Co., London).
6.
KawagutiM.‘Numerical solution of the Navier-Stokes equation for the flow in a two-dimensional cavity’, J. phys. Soc. Japan196116, (No. 11), 2307.
7.
BurggrafO. R.‘Analytical and numerical studies of the structure of steady separated flows’, J. Fluid Mech.196624, (No. 1), 113.
8.
BarakatH. Z.ClarkJ. A.‘Analytical and experimental study of the transient laminar natural convection flows in partially filled containers’, Proc. Third Int. Heat Transfer Conf., Chicago, 1966 (vol. 2, paper No. 57), 152.
9.
SimuniL. M.‘The numerical solution of some problems in the flow of a viscous fluid’, Inzh. Zh.19644, 446.
10.
StrandT.‘Inviscid incompressible flow theory of static two-dimensional solid jets in proximity to the ground’, J. aero. Sci.196229, (No. 2), 170.
11.
ChungP. M.ViegasJ. R.‘Heat transfer at the reattachment zone of separated laminar boundary layers’, N.A.S.A. TN D-1072, 1961.
12.
WolfshteinM.‘Convection processes in impinging jets’, Ph.D. Thesis, London University, 1968.
