zbMATH — the first resource for mathematics

Simulation of Taylor-Couette flow. I. Numerical methods and comparison with experiment. (English) Zbl 0561.76037
We present a numerical method that allows us to solve the Navier-Stokes equation with boundary conditions for the viscous flow between two concentrically rotating cylinders as an initial-value problem. We use a pseudospectral code in which all of the time-splitting errors are removed by using a set of Green functions (capacitance matrix) that allows us to satisfy the inviscid boundary conditions exactly. For this geometry we find that a small time-splitting error can produce large errors in the computed velocity field. We test the code by comparing our numerically determined growth rates and wave speeds with linear theory and by comparing our computed torques and wave speeds with experimentally measured values and with the values that appear in other published numerical simulations.

76D05 Navier-Stokes equations for incompressible viscous fluids
76M99 Basic methods in fluid mechanics
76-04 Software, source code, etc. for problems pertaining to fluid mechanics
Full Text: DOI
[3] DOI: 10.1086/157178
[4] DOI: 10.1017/S0022112071002246 · Zbl 0228.76076
[5] DOI: 10.1017/S0022112060000177 · Zbl 0173.28901
[6] DOI: 10.1017/S0022112068000029 · Zbl 0193.56502
[7] DOI: 10.1017/S0022112062001287 · Zbl 0116.19001
[8] DOI: 10.1017/S0022112065000241 · Zbl 0134.21705
[9] DOI: 10.1143/PTP.69.396
[10] Taylor, Phil. Trans. R. Soc. Lond. A 223 pp 289– (1923)
[11] DOI: 10.1016/0045-7930(78)90017-8 · Zbl 0387.76025
[12] DOI: 10.1017/S0022112058000276 · Zbl 0081.41001
[14] Mallock, Proc. R. Soc. Lond. A 45 pp 126– (1888)
[15] DOI: 10.1017/S002211206600079X
[17] Jones, J. Fluid Mech. 102 pp 253– (1981)
[18] DOI: 10.1016/0021-9991(79)90097-4 · Zbl 0397.65077
[20] DOI: 10.1017/S0022112074000541 · Zbl 0271.76027
[22] Orszag, J. Fluid Mech. 52 pp 524– (1984)
[23] DOI: 10.1016/0021-9991(83)90006-2 · Zbl 0529.76034
[24] DOI: 10.1016/0021-9991(80)90037-6 · Zbl 0425.76023
[25] DOI: 10.1063/1.1692432 · Zbl 0195.55403
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.