Computation of taylor vortex flow by a transient implicit method

Abstract A finite difference method is presented for the computation of steady axisymmetric solutions of Navier-Stokes equations using the time dependent stream function, vorticity, and tangential velocity formulation. The scheme involves implicit fractional steps and fast Fourier transforms. Upwind differencing for convective terms is used in order to increase the stability for high values of the Reynolds number. The method is applied to the flow in an annulus of rectangular cross section with rotating walls. Attention is focused upon the problem of centrifugal instabilities, non-uniqueness of the steady state solution, and selection of wavelengths in the supercritical range.