Analysis of different POD methods for PIV-measurements in complex unsteady flows

摘要

Proper Orthogonal Decomposition (POD) is an effective tool in fluid dynamics for investigation of complex, transitional or turbulent flows. In POD the transient vector or scalar field (velocity, concentration, temperature, etc.) is decomposed into a sum of spatial modes multiplied with time coefficients (Fourier-splitting method). However, these spatial modes and time coefficients can in practice be obtained by different methods. Even if POD has been used in numerous fluid dynamical studies, there are only few publications describing the relationship between the different methods and comparing the results. In the present case the POD basis functions are calculated either by Singular Value Decomposition (SVD) or by the Snapshot-POD approach. The results are compared in order to understand similarities and differences between the methods, as well as advantages and drawbacks. Comparisons between the obtained spatial modes, time coefficients, required computational effort, and complexity of calculation are presented and discussed. The influence of the numerical settings is also investigated, in particular the impact of the number of snapshots on the results. Finally, the differences obtained when analyzing a vector field globally or component-wise are discussed in detail.