It has been a challenge to simulate flexible flapping wings or other three-dimensional problems involving strong fluid–structure interactions. Solving a unified fluid–solid system in a monolithic manner improves both numerical stability and efficiency. The current algorithm considered a three-dimensional extension of an earlier work which formulated two-dimensional fluid–structure interaction monolithically under a unified framework for both fluids and solids. As the approach is extended from a two-dimensional to a three-dimensional configuration, a cell division technique and the associated projection process become necessary and are illustrated here. Two benchmark cases, a floppy viscoelastic particle in shear flow and a flow passing a rigid sphere, are simulated for validation. Finally, the three-dimensional monolithic algorithm is applied to study a micro-air vehicle with flexible flapping wings in a forward flight at different angles of attack. The simulation shows the impact from the angle of attack on wing deformation, wake vortex structures, and the overall aerodynamic performance.

中文翻译：

---

一种用于柔性扑翼流动模拟的整体算法

模拟灵活的扑翼或其他涉及强流固耦合的三维问题一直是一个挑战。以整体方式求解统一的流固系统可提高数值稳定性和效率。当前算法考虑了早期工作的三维扩展，该工作在流体和固体的统一框架下整体制定二维流固耦合。随着该方法从二维配置扩展到三维配置，细胞分裂技术和相关的投影过程变得必要，并在此处进行了说明。两个基准案例，剪切流中的松软粘弹性粒子和通过刚性球体的流，被模拟以进行验证。最后，应用三维单片算法研究了具有柔性扑翼的微型飞行器在不同攻角下向前飞行。仿真显示了攻角对机翼变形、尾涡结构和整体气动性能的影响。