Reduced Dimension Models for Hydrodynamical Systems: Experiment, Computation and Theory

流体动力系统的降维模型：实验、计算和理论

• 批准号: 0103863
• 负责人: Anette Hosoi
• 金额: $ 13.05万
• 依托单位: Harvey Mudd College
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-08-15 至 2002-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0103863&HistoricalAwards=false
• 关键词: Reduced; Dimension; Models; Hydrodynamical; Systems

This project is designed to develop reduced dimension models for hydrodynamical systems and to foster undergraduate participation in mathematical research. While the fundamental equations describing fluid motion, the Navier-Stokes equations, are well-known, it is generally computationally expensive and analytically infeasible to solve the full equations exactly. To better understand these systems, it is necessary to turn to simplified or reduced models resulting from systematic approximations of the full equations. The semi-discrete approximation techniques which are utilized in this project focus primarily on reducing the dimension of the full fluid equations by exploiting symmetries or widely disparate lengthscales in specific systems. The resulting predictions from the reduced models will be compared qualitatively and quantitatively with experimental data.Fluid dynamics arises in a multitude of biological, environmental and industrial applications. This project is designed to develop models that describe basic hydrodynamical phenomena such as hydraulic jumps that can arise in jet impingement cooling systems and hydrodynamical systems with flexible boundaries. The latter include spinning magnetic media such as disk drives, and biological problems such as insect flight, blood flow in arteries and dynamics of the syrinx in song birds. Undergraduate participation is an integral part of both the experimental and mathematical aspects of the program. Mathematical models will be tested in the new Fluid Dynamics Laboratory which will provide a hands-on environment in which students learn to integrate mathematics with physical phenomena. This unique approach encourages students to apply their mathematical skills in consort with their physical intuition within the framework of contemporary research.

该项目旨在为流体动力学系统开发降低的维度模型，并促进本科参与数学研究。尽管描述流体运动的基本方程式，但Navier-Stokes方程是众所周知的，但它通常在计算上昂贵且在分析上不可行，可以准确求解完整的方程式。为了更好地理解这些系统，有必要转向由完整方程式系统近似而产生的简化或简化模型。该项目中使用的半二散近似技术主要是通过利用对称性或在特定系统中的长度差异来降低全流体方程的维度。从还原模型的结果预测将与实验数据进行定性和定量比较。流量动力学在众多生物，环境和工业应用中产生。该项目旨在开发描述基本流体动力学现象的模型，例如在喷气撞击冷却系统和具有柔性边界的流体动力学系统中可能出现的液压跳跃。后者包括旋转磁媒体，例如磁盘驱动器，以及昆虫飞行，动脉流动和Syrinx动态的生物学问题。本科参与是该计划的实验和数学方面的组成部分。数学模型将在新的流体动力学实验室中进行测试，该实验室将提供一个动手的环境，学生学习将数学与物理现象相结合。这种独特的方法鼓励学生在当代研究的框架内将其数学技能运用在配偶中。