Three-Dimensional Time Resolved Lagrangian Flow Field Reconstruction Based on Constrained Least Squares and Stable Radial Basis Function

TL;DR

This paper introduces a novel 3D flow reconstruction method combining constrained least squares, stable radial basis functions, and partition-of-unity to accurately and robustly process large-scale Lagrangian particle tracking data, enabling high-resolution flow analysis.

Contribution

The paper presents a comprehensive 3D divergence-free flow reconstruction technique that directly processes scattered LPT data without conversions, integrating multiple algorithms for improved accuracy and scalability.

Findings

Achieves high-accuracy flow reconstruction from large LPT datasets.

Enables spatiotemporal super-resolution with physical constraints.

Validated with synthetic and experimental data showing robustness.

Abstract

The three-dimensional Time-Resolved Lagrangian Particle Tracking (3D TR-LPT) technique has recently advanced flow diagnostics by providing high spatiotemporal resolution measurements under the Lagrangian framework. To fully exploit its potential, accurate and robust data processing algorithms are needed. These algorithms are responsible for reconstructing particle trajectories, velocities, and differential quantities (e.g., pressure gradients, strain- and rotation-rate tensors, and coherent structures) from raw LPT data. In this paper, we propose a three-dimensional (3D) divergence-free Lagrangian reconstruction method, where three foundation algorithms -- Constrained Least Squares (CLS), stable Radial Basis Function (RBF-QR), and Partition-of-Unity Method (PUM) -- are integrated into one comprehensive reconstruction strategy. Our method, named CLS-RBF PUM, is able to (i) directly reconstruct flow fields at scattered data points, avoiding Lagrangian-to-Eulerian data conversions; (ii) assimilate the flow diagnostics in Lagrangian and Eulerian descriptions to achieve high-accuracy flow reconstruction; (iii) process large-scale LPT data sets with more than hundreds of thousand particles in two dimensions (2D) or 3D; (iv) enable spatiotemporal super-resolution while imposing physical constraints (e.g., divergence-free for incompressible flows) at arbitrary time and location. Validation based on synthetic and experimental LPT data confirmed that our method can consistently achieve the above advantages with accuracy and robustness.