A Numerical Procedure for Predicting Multiple Solutions of a Spherical Taylor-Couette Flow

A new numerical procedure for predicting multiple solutions of Taylor vortices in a spherical gap is presented. The steady incompressible Navier–Stokes equations in primitive variables are solved by a finite- difference method using a matrix preconditioning technique. Routes leading to multiple flow states are designed heuristically by imposing symmetric properties. Both symmetric and asymmetric solutions can be predicted in a deterministic way. The current procedure gives very fast convergence rate to the desired flow modes. This procedure provides an alternative way of finding all possible stable steady axisymmetric flow modes.