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Numerical simulation of three-dimensional Couette-Taylor flows. (English) Zbl 0949.76062
From the summary: To investigate the time-dependent non-axisymmetric flow between two rotating cylinders, or the so-called Couette-Taylor problem, we propose a numerical method to solve three-dimensional Navier-Stokes equations. First, the projection method is employed to obtain the pressure Poisson equation. Then the velocity is solved from the equations of motion by using a semi-implicit finite difference scheme. The numerical solution thus obtained has the accuracy of second-order in both time and space discretizations. We obtain the Couette-Taylor flow patterns from direct numerical simulation for the regimes of steady circular Couette flow, steady Taylor vortices, and for their intermediate processes, as well as the onset of periodic spiral vortices.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76U05 General theory of rotating fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
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[1] and , The Couette-Taylor Problem, Springer, New York, 1994. · Zbl 0817.76001 · doi:10.1007/978-1-4612-4300-7
[2] Couette, Ann. Chim. Phys. 6 pp 433– (1890)
[3] Taylor, Philos. Trans. R. Soc. Lond. Ser. A 223 pp 289– (1923) · doi:10.1098/rsta.1923.0008
[4] Andereck, J. Fluid Mech. 164 pp 155– (1986) · doi:10.1017/S0022112086002513
[5] Meyer-Spasche, J. Comp. Phys. 35 pp 100– (1980) · Zbl 0425.76023 · doi:10.1016/0021-9991(80)90037-6
[6] Cliffe, J. Fluid Mech. 135 pp 219– (1983) · Zbl 0599.76039 · doi:10.1017/S0022112083003055
[7] Fasel, J. Fluid Mech. 138 pp 21– (1984) · Zbl 0595.76022 · doi:10.1017/S0022112084000021
[8] Cliffe, J. Fluid Mech. 153 pp 243– (1985) · Zbl 0584.76117 · doi:10.1017/S0022112085001240
[9] and , ’A semi-implicit projection method for solving transient 3D flow in cylindrical co-ordinates system’ Proc. 2nd Asian Computational Fluid Dynamics Conference, Tokyo, Japan, 1996, pp. 319-324.
[10] Physical Fluid Dynamics, 2nd edn., Oxford University Press, New York, 1988.
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