  Continual perturbations to the flow field in the square lid driven cavity can
significantly impact both its stability and the dynamic characteristics of the
system. In this study, the effect of these perturbations are analyzed via
computational fluid dynamics simulations of a square, two-dimensional, lid
driven cavity containing varying area fractions of suspended particles. The
evolution over time of these particle-particle and particle-fluid interactions
generate two-dimensional disturbance velocity changes in the flow field. In
order to better understand the characteristics and effects of these changes,
proper orthogonal decomposition analysis is performed on the velocity
difference flow field to determine the dominant flow structures over the
simulation time domain. The resulting eigenvectors and eigenvalues represent
the varying dominant flow structures and their respective dominance over the
simulation time, respectively. This is carried out at particle suspension area
fractions from 10\% - 50\% and for Reynolds numbers of 100, 400, 700, and 1000.
Critical flow regimes and particle suspension area fractions are discussed in
order to characterize the stability of this particle-in-fluid system.
