This paper studies the interactions between Bingham fluids and flexible structures under an immersed boundary lattice-Boltzmann framework. The objective of this paper is to understand the rheology effects of Bingham fluids on the structure responses and the flow characteristics within Bingham fluids–structure interactions. To this end, a numerical algorithm that integrates the lattice Boltzmann method and the smoothed point interpolation method is proposed. Alongside this, a hybrid multiple relaxation time scheme in the framework of the immersed boundary-lattice Boltzmann method is used to improve the numerical accuracy and stability. Then, the numerical algorithm is applied to three typical fluid–structure interactions cases in both Newtonian and Bingham fluids regarding an elastic beam, a self-induced elastic beam attached to a circular cylinder and a self-propelled fishlike body. Numerical results highlight that the yield stress of Bingham fluids influences predominantly on the structure responses, such as the solid deformation, the oscillation amplitude, the oscillation period, and the swimming velocity. In addition, the yielded/unyielded zones' evolution process of the Bingham fluids–structure interaction is also identified in this paper.

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.

The influence of oblique currents in narrow and shallow channels causes the fluid flow around ships to become complex. To analyze the hydrodynamic characteristics of a ship in such channels, it is essential to examine the influence of oblique currents on the ship’s hydrodynamic characteristics. In this study, current direction, ship speed, current speed, and water depth were identified as determinants affecting the hydrodynamic characteristics of a ship. Numerical simulations were conducted on a large oil tanker to investigate the effects of these factors on the ship’s hydrodynamic characteristics. The viscous fluid flow was modeled using the unsteady Reynolds-averaged Navier–Stokes (URANS) equations in conjunction with the k-ε turbulence model. The URANS equations were discretized using the finite volume method. The numerical results indicate substantial differences in the hydrodynamic characteristics of ships under oblique current conditions compared to still-water conditions. At a current direction of β = −45°, the direction of the sway force is consistent with that of still water’s sway force, which is an attractive force. The yaw moment at β = −45° changes from a bow-out moment under still-water conditions to a bow-in moment. Conversely, at a current direction of β = 45°, the sway force shifts from an attractive force under still-water conditions to a repulsive force. The yaw moment acts as a bow-out moment, which is consistent with that observed in still-water conditions. Furthermore, the influence of hydrodynamic characteristics on a ship varies significantly with changes in ship speed, current speed, and water depth. To ensure the safe navigation of ships, it is essential to develop and apply comprehensive strategies and countermeasures that account for practical conditions.