This paper presents a study on streamline penetration, velocity error, and consequences of a fluid–structure interaction (FSI) solver based on the feedback immersed boundary method (IBM). In the FSI solver, the fluid dynamics is solved by the lattice Boltzmann method; the solid structure deformation is solved by the finite difference method and the finite element method for two- and three-dimensional cases, respectively; and the feedback IBM is used to realize the interaction between the fluid and the structure. The IBM is implemented in non-iterative and iterative ways. For the non-iterative version, two types of integration are discussed: without and with velocity prediction step. Five benchmark cases are simulated to study the performance of the three implementations: a uniform flow over a cylinder, flow-induced vibration of a flexible plate attached behind a stationary cylinder in a channel, flow through a two-dimensional asymmetric stenosis, a one-sided collapsible channel, and a three-dimensional collapsible tube. Results show that both the IBM with prediction step, the iterative IBM, and one iteration IBM with proper feedback coefficients can suppress the spurious flow penetration on the solid wall. While the velocity error does not significantly affect the force production and structure deformation for external flows, reducing it significantly improves the prediction of the force distribution and structure deformation for internal flows. In addition, the iterative IBM with smaller feedback coefficient has better numerical stability. This work will provide an important guideline for the correct use of the feedback IBMs.

Fluid-structure interaction (FSI) is a very common physical phenomenon which extensively exists in nature, human daily life and many engineering applications. The lattice Boltzmann method (LBM) is an alternative of solving Navier–Stokes equations to obtain complex fluid dynamics. Since the proposal of lattice Bhatnagar–Gross–Krookmodel, the LBM has been improved and applied to various complex flows ranging from laminar flow to turbulent flow and Newtonian flow to non-Newtonian flow. To handle the associated FSI, the bounce-back scheme was proposed and then the immersed boundary method (IBM) was incorporated into the LBM for the simplicity and robustness of IBM in handling complex and moving geometries and the significant efficiency of LBM in solving fluid dynamics. In recent years, the combined frameworks of LBM, that is, bounce-back–lattice Boltzmann method and immersed boundary–lattice Boltzmann method have witnessed a significant development and the successful applications can be found in a range of physical problems such as flow around bluff bodies, flapping wings, wind turbines, aeroacoustics, sea wave modelling and et al. In this paper, the recent progress of LBM and some typical applications involving FSI are reviewed.