Hopf bifurcation of the unsteady regularized driven cavity flow

Abstract A numerical simulation of the unsteady incompressible flow in the unit cavity is performed by using a Chebyshev-Tau approximation for the space variables. The high accuracy of the spectral methods and the condensed distribution of the Chebyshev-collocation points near the boundary enable us to obtain reliable results for high Reynolds numbers with a moderate number of modes. It is found that the flow converges to a stationary state for Reynolds numbers (Re) up to 10,000; for Reynolds numbers larger than a critical value 10,000

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