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 stream-function 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 have been reached. A discussion is included about the indicators that are used to show that an asymptotic state has been reached and to show that the asymptotic state is indeed periodic. © 1990.