Constrained Lagrangian and Hamiltonian Mechanics in Fluid-Body Interactions: Analytical Modeling and Computational Methods

流体相互作用中的约束拉格朗日和哈密顿力学：分析建模和计算方法

• 批准号: 1000652
• 负责人: Scott Kelly
• 金额: $ 20万
• 依托单位: University of North Carolina at Charlotte
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-15 至 2015-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1000652&HistoricalAwards=false
• 关键词: Constrained; Lagrangian; Hamiltonian; Mechanics; Fluid

This project advances a novel perspective on the theoretical and computational modeling of interactions among solid bodies and vortical fluids, illuminating the fundamental presence of integrable and nonintegrable constraints in Lagrangian and Hamiltonian descriptions of such interactions. The project focuses on four distinct topics: (1) the formal equivalence of gyroscopic lift forces to nonholonomic forces of constraint, (2) the mathematical treatment of conditions of flow attachment or stagnation as holonomic or nonholonomic constraints, (3) the resolution of the Hamiltonian structure underpinning interactions of free bodies with discrete vortex distributions into constrained and unconstrained components, and (4) the realization of variational integration methods which preserve balance principles between vortex shedding from solid surfaces and the corresponding development of surface forces.Problems involving the dynamic interaction of fluids with solid structures abound in the natural and engineered worlds. A deeper understanding of such interactions promises to improve the design of systems ranging from robotic vehicles to energy-harvesting devices, but the subtle physics underpinning such interactions presents challenges to traditional mathematical modeling methods. This project will explore fundamental parallels between the modeling of fluid-structure interactions and the modeling of other mechanical phenomena, with the goal of illuminating pervasive physical principles and novel analytical techniques.

这个项目在固体和涡旋流体之间相互作用的理论和计算建模方面提出了一个新的视角，阐明了这种相互作用的拉格朗日和哈密顿描述中基本存在的可积和不可积约束。该项目专注于四个不同的主题：(1)陀螺升力与非完整约束力的形式等价，(2)作为完整或非完整约束的流动附着或停滞条件的数学处理，(3)将支持自由物体与离散涡流分布相互作用的哈密顿结构分解为约束和非约束分量，以及(4)实现变分积分方法，保持从固体表面脱落的涡流与相应的表面力发展之间的平衡原则。涉及流体与固体结构的动态相互作用的问题在自然界和工程世界中比比皆是。对这种相互作用的更深入了解有望改进从机器人车辆到能源收集设备等各种系统的设计，但支撑这种相互作用的微妙物理给传统的数学建模方法带来了挑战。这个项目将探索流体-结构相互作用的建模与其他力学现象的建模之间的基本相似之处，目的是阐明普遍存在的物理原理和新的分析技术。