Fluid–structure interaction (FSI) plays a crucial role in various scientific and engineering fields, particularly in biomechanics. A lattice Boltzmann (LB) model is developed to investigate the coupled dynamics of fluid–structure systems within a fully Eulerian framework. In this model, one LB equation captures the evolution of a diffuse interface that smoothly interpolates physical properties across phases. This yields unified mass and momentum conservation equations for the continuum dynamics, which are solved by the other LB equation. To close the system, the evolution of the left Cauchy–Green tensor is introduced to compute the elastic stresses. Validation and verification are performed through comparisons with analytical solutions and benchmark problems, confirming the model's accuracy and robustness. The model is further employed to explore bile flow dynamics in the post-cholecystectomy bile duct, with particular attention to the influence of shear modulus variations and the temporal evolution of flow patterns under external compression-induced stenosis. The results highlight the model's ability to handle complex geometries and large deformations, demonstrating its potential as a robust tool for a wide range of FSI problems in biomechanics.
Wu et al. (Thu,) studied this question.