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，结合实验，在中等尺度上研究流体中的生物推进。这些问题通常涉及在惯性和粘度都很重要的流体中柔性附属物的运动。与这些问题相关的基本计算挑战是准确和有效地模拟周围流体中运动的柔性结构。一个目标是将斯托克斯流的数值方法扩展到1到10数量级的雷诺数。这些方法将被应用于空气动力学问题，包括气流通过刚毛翼。另一个目标是将粘性效应纳入旋涡片方法，以便在更大范围内更准确地模拟流动。然后，这些工具将用于了解主动控制鱼鳍和其他流体与生物体相互作用的重要性。最后，这项工作将允许在广泛的雷诺数范围内比较推进机制和数值方法。本研究项目建立的数值方法和模型可以应用于许多不同的生物流固相互作用问题。除了这些具体的建议之外，还有一些例子包括心脏的血液输送，肺部的空气流动，柔性材料（如叶子和无根生物）的阻力减少，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对推进力学的理解，可以用于微型空气和水交通工具的设计；用于研究生物学优化问题的计算工具的发展；丰富的非线性动力学物理实例；指导本科生进行实验和建模工作，指导研究生进行计算和建模研究。外展部分将帮助更多的学生通过独立的研究项目实现自主研究和批判性思维。该项目还解决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?''