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Proper Orthogonal Decomposition for Time-Dependent Lid-Driven Cavity Flows

Proper orthogonal decomposition (POD) is employed to study a time-dependent lid-driven cavity flow. Ensembles of data are compiled from transient solutions computed with different grids and Reynolds numbers. The POD bases are used to reconstruct the constituents of the ensemble. Error measures are used to evaluate the effectiveness of the method. The geometric locations of major errors and their dependency on Reynolds number are also investigated. The POD technique proves capable of capturing more than 99.7% of the kinetic energy, using the first three eigenmodes. The errors were found to be uniformly bounded, which validates the theory derived.