Abstract
Abstract We present a multigrid-continuation method for computing the transition from two-dimensional Taylor-vortex to three-dimensional wavy-vortex flow in the Taylor experiment. The method is also used to continue the path of travelling wave solutions as the Reynolds number is varied. The steady Navier-Stokes equations in a rotating frame of reference and an integral constraint are approximated by second-order accurate finite differences. For the convective terms in the conservation equations an upwind discretization controlled by the eigenvalues of their Jacobians is used. An iterative method for finding the speed of the travelling wave involves switching between the unsteady equations and the steady equations in a rotating frame. This is used only once to get the first wavy-vortex solution. A comparison of the results with experimental and numerical data shows good accuracy for the method and the validity of the travelling-wave formulation.
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