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.

中文翻译：

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扑动昆虫翅膀被动羽化和拱形的计算流固耦合框架

在扑动的昆虫翅膀中，静脉支撑着柔性的翼膜，使得翅膀通过大的弹性变形被动地形成羽化和弯曲运动。这些运动对于昆虫扑动飞行的不稳定空气动力学至关重要。因此，这种现象的潜在机制是昆虫飞行研究的一个重要问题。对描述这些弹性变形的模型机翼与周围流体之间的强耦合进行系统参数研究，这是这种现象的直接表述，将有效解决这个问题。本研究的目的是为这些系统参数研究开发一个强大的数值框架。所提出的框架由两种新颖的数值方法组成：（1）一种针对整体流固耦合（FSI）方程组使用代数分裂和半隐式格式的完全并行求解方法，该方法对于各种属性都具有数值稳定性，例如例如固体与流体的质量比和大的身体运动以及大的弹性变形。（2）采用像素建模（像素模型翼）的昆虫扑翼结构力学模型，与显式节点定位相结合，可显着降低控制流体网格的计算成本。对于一些基准问题和结合实际昆虫数据的动态缩放模型，证明了所提出框架的有效性。最后，通过对在各种固液质量比的流体中扑动的像素模型翅膀的参数研究，我们发现了扑动昆虫翅膀的羽化和弧度运动的 FSI 机制。