A NUMERICAL STUDY OF THE AXISYMMETRICAL COUETTE-TAYLOR PROBLEM USING A FAST HIGH-RESOLUTION 2ND-ORDER CENTRAL SCHEME

We present a numerical study of the axisymmetric Couette-Taylor proble m 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 i s readily adaptable to other geometries and to more complicated flows. The scheme exhibits competitive performance in terms of accuracy, res olution, and robustness. The numerical results agree accurately with l inear stability theory and with previous numerical studies.