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Vorticity-velocity formulation for high Re flows. (English) Zbl 0616.76034
A very accurate ADI method has been applied to the Navier-Stokes equations written in vorticity-velocity variables. Centered in space finite differences reduce the system of P.D.E.’s to an algebraic system of block tridiagonal form. The equations are strongly coupled and they do not require an iterative procedure to obtain a solenoidal velocity field. The present numerical method, with a non-uniform mesh, predicts very good solutions for the driven cavity flow and for the flow over a backward- facing step at high Re using a limited number of calculation points.

76D05 Navier-Stokes equations for incompressible viscous fluids
76M99 Basic methods in fluid mechanics
Full Text: DOI
[1] Kim, J.; Moin, M., Application of a fractional-step method to incompressible Navier-Stokes equations, J. comput. phys., 59, 308-323, (1985) · Zbl 0582.76038
[2] Wong, A.K.; Retzes, J.A., An effective vorticity-vector potential formulation for the numerical solutions of three-dimensional duct flow problems, J. comput. phys., 55, 98-114, (1984) · Zbl 0533.76026
[3] Fasel, H., Investigation of boundary layers by a finite difference model of the Navier-Stokes equations, J. fluid mech., 78, 353-383, (1976) · Zbl 0404.76041
[4] Dennis, S.C.R.; Ingham, D.B.; Cook, R.N., Finite-difference methods for calculating steady incompressible flows in three dimensions, J. comput. phys., 33, 325-339, (1979) · Zbl 0421.76019
[5] Gatski, J.B.; Grosch, C.E.; Rose, M.E., A numerical study of the two-dimensional Navier-Stokes equations in vorticity-velocity variables, J. comput. phys., 48, 1-22, (1982) · Zbl 0502.76040
[6] Lilly, D.K., On the computational stability of numerical solutions of time-dependent non-linear geophysical fluid dynamics problems, Mon. weather rev., 93, 11-26, (1965)
[7] Orlandi, P., Application of vorticity-velocity formulation for engineering and geophysical flows, () · Zbl 0627.76036
[8] Cheng, S.I., A new look on turbulent shear flows, ()
[9] Guj, G.; Stella, F., A numerical solution of high re numbers recirculating flows in vorticity-velocity form, () · Zbl 0672.76031
[10] Thompson, H.D.; Webb, B.W.; Hoffman, J.D., The cell Reynolds number myth, Int. J. num. meth. fluids, 5, 305-310, (1985) · Zbl 0586.76056
[11] Koseff, J.R.; Street, R.L., Visualization studies of a shear driven three-dimensional recirculating flow, Trans. ASME, J. fluid engng, 106, 21-29, (1984)
[12] Ghia, U.; Ghia, K.N.; Shin, C.T., High-re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, J. comput. phys., 48, 387-411, (1982) · Zbl 0511.76031
[13] Winters, K.H.; Cliffe, K.A., A finite element study of laminar flow in a square cavity, UKAERE harwell report R-9444, (1979) · Zbl 0535.76093
[14] Benjamin, A.S.; Denny, V.E., On the convergence of numerical solutions for 2-D flows in a cavity at large re, J. comput. phys., 33, 340-358, (1979) · Zbl 0421.76020
[15] Orlandi, P.; Briscolini, M., Direct simulation of burgulence, CTAC ’83, (), 641-652 · Zbl 0577.76056
[16] Armally, B.F.; Durst, F.; Pereira, J.C.; Schomung, B., Experimental and theoretical investigation of backward-facing step flow, J. fluid mech., 127, 473-496, (1983)
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