Currently, the immersed boundary method (IBM) is widely used in fluid–structure interaction simulations. However, due to the fact that the mesh used in IBM is often fixed, when the motion or deformation range of the object is large, it causes significant waste of computing resources. We combine a fluid simulation method based on IBM and adaptive mesh refinement with a structural solver to form an efficient computational framework suitable for three-dimensional fluid–structure interaction. Three complex fluid–structure interaction cases are tested, including a flapping flag in a free stream, an inverted flag in a free stream, and an elastic wing for hovering motion. The results show that the framework significantly reduces the number of fluid mesh cells compared to fixed mesh cases (with a reduction of more than 60%) while meeting accuracy requirements. Finally, this computational framework was used to simulate the flapping of flexible wings in a butterfly model. Flexible wings are composed of skeletons and membranes. The results indicate that leading-edge vortices are generated on the inner and outer sides of the flexible wing during the downstroke, which increases the lift during the downstroke. However, during the upstroke, the leading-edge vortices and trailing edge vortices of the flexible wing are stronger, thereby increasing the thrust during the upstroke.
Wang et al. (2026) studied this question.