Iterative modal reconstruction for sparse particle tracking data

Abstract

A method to reconstruct the dense velocity field from relatively sparse particle tracks is introduced. The approach leverages the properties of proper orthogonal decomposition (POD), and it iteratively reconstructs the detailed spatial modes from a first, coarse estimation thereof. The initially coarse Cartesian representation of the velocity field is obtained by local data averaging, where POD is applied. The spatial resolution of the POD modes is enhanced by reprojecting them onto the sparse particle velocity to iteratively improve the reconstruction of the temporal coefficients. Finally, the enhanced velocity field is represented at high-resolution with a reduced order model using the dominant POD modes. The method is referred to as iterative modal reconstruction (IMR), as an extension of the recently proposed data-enhanced particle tracking velocimetry algorithm, introduced for cross correlation-based velocity data. Experiments in the wake of a cylinder at ReD = 27 000 are used to assess the suitability of the method to resolve the turbulent Kármán–Benard wake. The approach is benchmarked against traditional as well as state-of-the-art reconstruction methods, illustrating the capability of IMR of enhancing the spatial resolution of sparse velocity data.