arXiv subjects

Lanyu Li

Publications and source records attributed to Lanyu Li.

4 recordsLinked to original sources

arXiv2024

Revisiting Liu and Katz (2006) and Zigunov and Charonko (2024b): on the Equivalence of the Omnidirectional Integration and the Pressure Poisson Equation

In this work, we demonstrate the equivalency of the Rotating Parallel Ray Omnidirectional Integration (RPR-ODI) and the Pressure Poisson Equation (PPE) for pressure field reconstruction from corrupted image velocimetry data (dubbed 'ODI $\equiv$ PPE'). Building on the work by Zigunov and Charonko (2024b), we show that performing the ODI is equivalent to pursuing the minimum norm least squares (MNLS) or minimum norm (MN) solution to a Poisson equation with all Neumann boundary conditions. By looking through the lens of linear algebra, regression, optimization, and the well-posedness of the Poisson equation, we provide a comprehensive and integrated framework to analyze ODI/PPE-based pressure field reconstruction methods. The new comprehensions on ODI $\equiv$ PPE provides theoretical and computational insights valuable to experimentalists beyond reducing the high computational cost of ODI to that of PPE. More importantly, we i) provide a comprehensive guideline for robust pressure reconstruction, and ii) unveil the shared strengths and limitations of ODI and PPE, which are elaborated in remarks and notes throughout this work. Some remarks suggest simple regularization strategies that serve as 'minimal reproducible examples' and provide a foundation for further refinement. This work paves the way for further improvements in ODI/PPE-based pressure field reconstruction by utilizing the extensive literature on fast and robust elliptic solvers as well as their associated regularization methods. Numerical experiments are presented to support and illustrate these arguments.

physics.flu-dyn↗

arXiv2024

Error propagation of direct pressure gradient integration and a Helmholtz-Hodge decomposition based pressure field reconstruction method for image velocimetry

Recovering pressure fields from image velocimetry measurements has two general strategies: i) directly integrating the pressure gradients from the momentum equation and ii) solving or enforcing the pressure Poisson equation (divergence of the pressure gradients). In this work, we analyze the error propagation of the former strategy and provide some practical insights. For example, we establish the error scaling laws for the Pressure Gradient Integration (PGI) and the Pressure Poisson Equation (PPE). We explain why applying the Helmholtz-Hodge Decomposition (HHD) could significantly reduce the error propagation for the PGI. We also propose to use a novel HHD-based pressure field reconstruction strategy that offers the following advantages or features: i) effective processing of noisy scattered or structured image velocimetry data on a complex domain; ii) using Radial Basis Functions (RBFs) with divergence/curl-free kernels to provide divergence-free correction to the velocity fields for incompressible flows and curl-free correction for pressure gradients; and iii) enforcing divergence/curl-free constraints without using Lagrangian multipliers. Complete elimination of divergence-free bias in measured pressure gradient and curl-free bias in the measured velocity field results in superior accuracy. Synthetic velocimetry data based on exact solutions and high-fidelity simulations are used to validate the analysis as well as demonstrate the flexibility and effectiveness of the RBF-HHD solver.

physics.flu-dyn↗

arXiv2024

A Simple Boundary Condition Regularization Strategy for Image Velocimetry Based Pressure Field Reconstruction

We propose a simple boundary condition regularization strategy to reduce error propagation in pressure field reconstruction from corrupted image velocimetry data. The core idea is to replace the canonical Neumann boundary conditions with Dirichlet ones obtained by integrating the tangential part of the pressure gradient along the boundaries. Rigorous analysis and numerical experiments justify the effectiveness of this regularization.

physics.flu-dyn↗

arXiv2023

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

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.

physics.flu-dyn↗