Hopf bifurcation in the driven cavity

Incompressible two dimensional calculations are reported for the impulsively started lid driven cavity with aspect ratio two. The algorithm is based on the time dependent streamfunction equation, with a Crank-Nicolson differencing scheme for the diffusion terms, and with an Adams-Bashforth scheme for the convection terms. A multigrid method is used to solve the linear implicit equations at each time step. Periodic asymptotic solutions have been found for Re = 10000 and for Re = 5000. The Re = 5000 results are validated by grid refinement calculations. The solutions are shown to be precisely periodic, and care is taken to demonstrate that asymptotic states were reached. A discussion is included about the indicators that are used to show that an asymptotic state was reached, and to show that the asymptotic state is indeed periodic.