Improved Proper Orthogonal Decomposition for Noise Reduction in Particle Flow Simulations*

Proper orthogonal decomposition (POD), widely utilised for turbulent flows, has recently been explored for processing particle data. An extension of the method based on time-windows offers a useful approach for noise reduction in particle simulations. However, to successfully remove statistical noise from the system, large amounts of data need to be provided. Moreover, POD can fail to improve the quality of an ensemble mean (statistical average) when applied to steady-state simulations. In order to achieve a better efficiency of POD in processing non-stationary fields, we have combined the method with wavelet-based filtering. In this new procedure, the wavelet thresholding is performed within POD's domain. In case of stationary problems, we will show how effectively POD can be applied to a matrix constructed from the mean, following the application of singular spectral analysis (SSA). The combination of POD and SSA is shown to successfully smooth time-dependent observables. Simulations were undertaken to illustrate the performance of the new tools applied to noisy velocity and density fields. Numerical examples include molecular dynamics, dissipative particle dynamics simulations of force-driven fluid flows and phase separation phenomena.