Global two-dimensional stability of the staggered cavity flow with an HOC approach

In this paper, we have carried out a global stability analysis of the flow inside a two sided staggered lid-driven cavity for both the parallel and anti-parallel motions of the lids. A fourth order spatially accurate and second order temporally accurate compact scheme is used to discretize the two-dimensional Navier–Stokes equations governing the flow as well as the perturbed equations leading to the generalized eigenvalue problem. Estimates of the critical parameters are found for several grids and extensive grid convergence study is performed to accurately identify them. Computation is performed for a wide range of Reynolds numbers (Re) on either side of the critical values in the range 50≤Re≤12,00050≤Re≤12,000. For flows below the critical Reynolds number RecRec, our numerical results are compared with established steady-state results and an excellent agreement is obtained in all the cases. For Reynolds numbers above RecRec, phase plane and spectral density analysis confirmed the existence of periodic and chaotic flow patterns.