K-nearest neighbors-enhanced shared time information multivariate proper orthogonal decomposition: Insights into particle migration in fluid flows

Multiscale spatiotemporal feature analysis of three-dimensional particle migration is crucial for elucidating the mechanisms between settling dynamics and fluid flow. To fully understand this complex system, we propose a multi-stage, multivariable analysis framework that combines an improved modal decomposition with low-dimensional dynamical modeling. In particular, by integrating a K-nearest neighbors algorithm into the shared time-information multivariable proper orthogonal decomposition, the K-nearest neighbors-enhanced shared time information multivariable proper orthogonal decomposition is used to enhance mode reconstruction accuracy and ensure consistent physical interpretation across velocity, pressure, and vorticity fields. Based on this low-dimensional representation of the flow, we then apply the sparse identification of nonlinear dynamics method to derive a system of ordinary differential equations that accurately captures the flow's underlying dynamics, enabling high-fidelity multivariable time-series prediction. Through multi-state clustering and modal feature analysis, we further reveal distinct stages and their spatiotemporal evolution during particles settling. Sedimentations of a single and dual particles are numerically simulated using the immersed boundary-lattice Boltzmann method, thereby providing a high-resolution flow field dataset for modal decomposition and mode reconstruction. Experimental results highlight that our approach is capable of capturing the complex multiscale dynamics of the flow. Moreover, with rapid, precise reconstruction and prediction being achieved, this paper provides a powerful tool for deeper understanding and control of particle migration dynamics.