POD Snapshot Data Reduction For Periodic Fluid Flows

Numerical simulations of turbulent flow require using a large spatial grid and very small time step increments. Dealing with the data set of the results using POD requires a long time. In this study, the minimum number of snapshots that can be used in POD is investigated via a proposed algorithm. This algorithm is based on linking the POD snapshots selection with the frequency content of the fluid flow variables. The reconstructed data set using the minimum snapshots is compared with the original data set. The comparison shows that the proposed algorithm can be used effectively to reduce the number of snapshots required by POD without affecting much the frequency content of the original data set. The effect of the snapshots reduction on the POD modes is investigated. The amplitude of the temporal POD modes and the singular values change as the number of snapshots changes but the product of them is almost constant for the same data set. Nomenclature f = frequency ac f = error band frequency c f = cutoff frequency , max FFT f = maximum frequency calculated using FFT j f = frequency of the jet exit velocity p f = predicted frequency using FFT sp f = spacing frequency f ∞ = frequency of the mainstream inlet velocity NFFT = number of FFT points Nds = number of data samples m = number of data point in each POD snapshot n = number of POD snapshots RMS = Root Mean Square S = singular value t = time s t = time step U = POD temporal mode i U = mean velocity component