A Numerical Study of the Axisymmetric Couette--Taylor Problem Using a Fast High-Resolution Second-Order Central Scheme

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Abstract
We present a numerical study of the axisymmetric Couette--Taylor problem using a finite difference scheme. The scheme is based on a staggered version of a second-order central-differencing method combined with a discrete Hodge projection. The use of central-differencing operators obviates the need to trace the characteristic flow associated with the hyperbolic terms. The result is a simple and efficient scheme which is readily adaptable to other geometries and to more complicated flows. The scheme exhibits competitive performance in terms of accuracy, resolution, and robustness. The numerical results agree accurately with linear stability theory and with previous numerical studies.