Computational fluid–structure interaction framework for passive feathering and cambering in flapping insect wings

In flapping insect wings, veins support flexible wing membranes such that the wings form feathering and cambering motions passively from large elastic deformations. These motions are essentially important in unsteady aerodynamics of insect flapping flight. Hence, the underlying mechanism of this phenomenon is an important issue in studies on insect flight. Systematic parametric studies on strong coupling between a model wing describing these elastic deformations and the surrounding fluid, which is a direct formulation of this phenomenon, will be effective for solving this issue. The purpose of this study is to develop a robust numerical framework for these systematic parametric studies. The proposed framework consists of two novel numerical methods: (1) A fully parallelized solution method using both algebraic splitting and semi‐implicit scheme for monolithic fluid–structure interaction (FSI) equation systems, which is numerically stable for a wide range of properties such as solid‐to‐fluid mass ratios and large body motions, and large elastic deformations. (2) A structural mechanics model for insect flapping wings using pixel modeling (pixel model wing), which is combined with explicit node‐positioning to reduce computational costs significantly in controlling fluid meshes. The validity of the proposed framework is demonstrated for some benchmark problems and a dynamically scaled model incorporating actual insect data. Finally, from a parametric study for the pixel model wing flapped in fluid with a wide range of solid‐to‐fluid mass ratios, we find a FSI mechanism of feathering and cambering motions in flapping insect wings. We developed a novel computational framework that consists of a fully parallelized solution method using algebraic splitting and semi‐implicit scheme for monolithic FSI equation systems, the parallel CG method, and a pixel model wing combined with explicit node‐positioning. Using the proposed framework, we found that feathering and cambering motions in flapping insect wings will be given based on the equilibrium between wing's elastic and aerodynamic forces, and these motions are enhanced by the wing's inertial force.