Meshless track assimilation (MTA) of 3D PTV data

Abstract We propose a data assimilation algorithm to improve the resolution of 3D particle tracking velocimetry (PTV) data and, as a byproduct, it estimates the pressure field. The proposed method, called meshless tracking assimilation (MTA), does not rely on a mesh to compute derivatives. Instead, it exploits the analytical formulation of the obtained field to extract the gradients of the involved quantities in arbitrary points. MTA actively constraints PTV data points to satisfy the Navier–Stokes equations in both time and space at user-defined spatial locations. Three test cases are investigated. The first one is a synthetic dataset reconstructed from a direct numerical simulation and it serves to ensure that the method is properly implemented and working. The second one is the 2020 data assimilation challenge which gives a qualitative comparison with other data assimilation methods. Finally, MTA is used on a Tomographic PTV experiment of a Jet Flow with R e D ≃ 3000 to ensure it can be implemented successfully on experimental data. The first and third test cases show a significant performance boost compared to the classic linear interpolation. This improvement allows for a higher level of structural resolution without sacrificing the temporal and spatial smoothness of the solution. The second test case generally aligns well with other state-of-the-art data assimilation techniques in terms of performance, but there are some noticeable differences.