POD Applied to Numerical Study of Unsteady Flow Inside Lid-Driven Cavity (Journal of Mathematical Study, 2018)
Flow inside a lid-driven cavity (LDC) is studied here to elucidate bifurcationsequences of the flow at super-critical Reynolds numbers $(Re_{cr1})$ with the help of analyzingthe time series at most energetic points in the flow domain. The implication of $Re_{cr1}$ in the context of direct simulation of Navier-Stokes equation is presented here forLDC, with or without explicit excitation inside the LDC. This is aided further by performingdetailed enstrophy-based proper orthogonal decomposition (POD) of the flowfield. The flow has been computed by an accurate numerical method for two differentuniform grids. POD of results of these two grids help us understand the receptivityaspects of the flow field, which give rise to the computed bifurcation sequences by understandingthe similarity and differences of these two sets of computations. We showthat POD modes help one understand the primary and secondary instabilities notedduring the bifurcation sequences.
Keywords: Lid driven cavity; POD; POD modes analysis; DNS; multiple Hopf bifurcation; polygonal core vortex.