Bifurcation analysis of incompressible flow in a driven cavity by the Newton–Picard method

Knowledge of the transition point of steady to periodic flow is becoming increasingly important in the study of laminar–turbulent flow transition or fluid–structure interaction. Such knowledge becomes available through the Newton–Picard method, a method related to the recursive projection method. Here, this method is applied to study the bifurcation behavior of the flow in a driven cavity between Reynolds number 7500 and 10,000. For the time discretization the θ-method is used and for the space discretization a robust finite-volume method. The implicit relations occurring after linearization are solved by the multilevel ILU solver MRILU. The results presented in this paper confirm findings from earlier work with respect to the transition point. They give more detailed information on unstable modes and clarify time series found by others.