Abstract
The Proper Orthogonal Decomposition (POD) is one of the most popular methods for discovering patterns from data in fluid mechanics. When the data is available on a uniform grid, such as in cross-correlation-based particle image velocimetry, the POD is equivalent to a Singular Value Decomposition (SVD) of the matrix containing the measurement. When the data is scattered, as in particle tracking velocimetry, the POD computation first requires interpolation onto a grid. Such interpolation degrades spatial resolution and limits the benefits of PTV over correlation-based methods. In this work, we propose a method to compute the POD from scattered data that circumvents the need for interpolation. The method uses physics-constrained Radial Basis Function (RBFs) regression to compute inner products in space and time. We demonstrate that this method is more accurate than the traditional interpolation or binning-based approaches. Since the method does not require the definition of a mesh and produces results that are analytic and mesh-independent, we refer to our method as meshless POD.
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