Collaborative Research: New models and numerical methods for flexible wings, fins, and membranes

该项目的目标是创建分析和计算工具，并结合实验，在中等尺度上研究流体中的生物推进。这些问题通常涉及柔性附件在流体中的运动，其中惯性和粘度都很重要。与这些问题相关的基本计算挑战是准确和高效地模拟周围流体中移动的、灵活的结构。其中一个目标是将Stokes流动的数值方法推广到1到10个数量级的雷诺数。然后这些方法将被应用于涉及通过刚毛机翼的流动的空气动力学问题。另一个目标是将粘性效应引入涡片方法，以便在更大范围的尺度上更准确地模拟流动。然后，这些工具将被用来理解主动控制鱼鳍射线和其他流体与生物体相互作用的情况的重要性。最后，这项工作将允许在广泛的雷诺数范围内对推进机制和数值方法进行比较。本研究项目中开发的数值方法和模型可以应用于众多不同的生物流固相互作用问题。除了那些特定于该提案的例子外，还有一些例子包括心脏泵血、空气在肺中流动、树叶和固着生物等柔性材料的减阻以及种子在空气中的传播和幼虫在水中的传播。这项工作的广泛影响包括：提高了对可用于微型空气和水飞行器设计的推进力学的理解；开发了有助于研究生物学优化问题的计算工具；丰富了物理非线性动力学的例子；为本科生提供了实验和建模工作的研究指导，并为研究生提供了计算和建模研究的指导。推广部分将帮助更多的学生通过独立的研究项目实现研究和批判性思维的自主性。这个项目还回答了美国国家科学院提出的关于理论在推进21世纪生物学中的作用的七个问题之一：“生命的工程学原理是什么？”

The goals of this project are to create analytical and computational tools, coupled with experiments, to investigate biological propulsion in fluids at intermediate scales. These problems typically involve the movement of a flexible appendage in a fluid where both inertia and viscosity are important. The fundamental computational challenge associated with these problems is the accurate and efficient simulation of the moving, flexible structure in the surrounding fluid. One aim is to extend numerical methods for Stokes flow to Reynolds numbers on the order of 1 to 10. These methods will then be applied to aerodynamics problems involving flow through bristled wings. Another aim is to incorporate viscous effects into vortex sheet methods, in order to more accurately simulate flows over a wider range of scales. These tools will then be used to understand the importance of active control of fish fin rays and other instances of fluid interactions with organisms. Finally, this work will allow for comparisons of propulsion mechanisms and numerical methods across a wide range of Reynolds numbers.The numerical methods and models developed in this research project can be applied to numerous and diverse biological fluid-structure interactions problems. Some examples beyond those specific to the proposal include the pumping of blood by the heart, the flow of air in the lungs, drag reduction in flexible materials such as leaves and sessile organisms, and the dispersal of seeds in air and larvae in water. The broader impacts of this work include the improved understanding of propulsion mechanics that can be used for the design of micro air and water vehicles; the development of computational tools which are useful to study optimization questions in biology; rich examples of nonlinear dynamics for physics; research mentoring to undergraduates in experimental and modeling work and graduate students in computational and modeling research. The outreach component will help more students achieve autonomy in research and critical thinking through independent research projects. This project also addresses one of the seven questions posed by the National Academy of Sciences on the role of theory in advancing 21st century biology: ``what are the engineering principles of life?''