Dynamic Stability and Multiscale Computation of 3D Incompressible Flows.
3D 不可压缩流的动态稳定性和多尺度计算。
基本信息
- 批准号:0713670
- 负责人:
- 金额:$ 31.38万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2007
- 资助国家:美国
- 起止时间:2007-09-01 至 2010-08-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The investigator and his colleagues study two fundamental problems in fluid dynamics. The first one is the dynamic stability property of 3D incompressible flows. The second one is to derive a systematic multiscale model to simulate the long time solution of the 3D Navier-Stokes equations. The dynamic stability property of the 3D incompressible Euler or Navier-Stokes equations plays a very important role in our understanding of the fluid dynamic stability and dynamic depletion of nonlinear vortex stretching. For a long time, many experts had believed that the nonlinear vortex stretching term is mostly a destabilizing term, which may lead to a finite time singularity of the 3D Euler or Navier-Stokes equations with a smooth initial condition.In this proposal, the investigator proposes a new strategy to study the dynamic stability of fluid flows by exploiting the anisotropic scaling of the singular support and the local solution structure. Furthermore, the investigator proposes a new multiscale model for the 3D Navier-Stokes equations by using a reparameterization of the solution in the frequency space and a nested multiscale expansion with a multiscale phase function. Careful numerical experiments will be performed to validate the multiscale model against direct numerical simulations and study the statistical properties of turbulent flows using the proposed multiscale model.Many fascinating natural phenomena such as tornadoes, hurricanes, typhoons, and tsunami waves are governed by the Navier-Stokes equations. The understanding of the solution behavior of the Navier-Stokes equations and the development of efficient computational methods to simulate their solutions have a tremendous impact in improving the national technology and for the well-being of the society.The advances in the proposed research could potentially improve the ability in weather forecasting, studying environmental change, and in predicting natural disasters.The proposed study on the dynamic stability and dynamic depletion of vortex stretching could lead to important insights on the large time behavior of the incompressible flows. This is one of the major open problems in physics and science. A systematic multiscale analysis could lead to a new generation of multiscale computational method to simulate turbulent flows, with potential for great impact throughout science and technology. An additional impact of this project will be the involvement of graduate students and postdoctoral fellows. The proposed research provides a solid training in mathematical analysis, physical modeling and numerical simulation. The interdisciplinary training they receive in this project will be very important for careers in mathematics and science.
这位研究者和他的同事研究了流体动力学中的两个基本问题。第一个问题是三维不可压缩流动的动力稳定性。第二部分是建立一个系统的多尺度模式,模拟三维Navier-Stokes方程的长时间解。三维不可压Euler或Navier-Stokes方程的动力学稳定性对于我们理解流体动力学稳定性和非线性涡拉伸的动力学损耗有着非常重要的作用。长期以来,许多学者认为非线性涡拉伸项主要是一个失稳项,它可能导致具有光滑初始条件的三维Euler或Navier-Stokes方程的有限时间奇异性,本文提出了一种利用奇异支撑的各向异性尺度和局部解结构来研究流体流动动力稳定性的新策略.此外,研究者提出了一个新的多尺度模型的三维Navier-Stokes方程通过使用在频率空间和嵌套的多尺度扩展与多尺度相函数的解决方案的重新参数化。我们将进行细致的数值实验,以验证多尺度模型与直接数值模拟的对比,并使用所提出的多尺度模型研究湍流的统计特性。许多迷人的自然现象,如龙卷风、飓风、台风和海啸波都由Navier-Stokes方程控制。了解Navier-Stokes方程的解的行为和开发有效的计算方法来模拟它们的解,对提高国家技术和社会福祉有着巨大的影响。拟议研究的进展可能会提高天气预报,研究环境变化,对涡拉伸的动态稳定性和动态损耗的研究,对不可压流动的大时间行为有重要的启示。这是物理学和科学中的一个主要开放问题。系统的多尺度分析可能会导致新一代的多尺度计算方法来模拟湍流,并可能对整个科学和技术产生重大影响。该项目的另一个影响将是研究生和博士后研究员的参与。该研究为数学分析、物理建模和数值模拟提供了坚实的基础。他们在这个项目中接受的跨学科培训将对数学和科学的职业生涯非常重要。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Thomas Hou其他文献
On the stability of the unsmoothed Fourier method for hyperbolic equations
- DOI:
10.1007/s002110050019 - 发表时间:
1994-02-01 - 期刊:
- 影响因子:2.200
- 作者:
Jonathan Goodman;Thomas Hou;Eitan Tadmor - 通讯作者:
Eitan Tadmor
On DoF Conservation in MIMO Interference Cancellation Based on Signal Strength in the Eigenspace
基于特征空间信号强度的MIMO干扰消除中自由度守恒
- DOI:
10.1109/tmc.2021.3126449 - 发表时间:
2023 - 期刊:
- 影响因子:7.9
- 作者:
Yongce Chen;Shaoran Li;Chengzhang Li;Huacheng Zeng;Brian Jalaian;Thomas Hou;Wenjing Lou - 通讯作者:
Wenjing Lou
Minimizing Age of Information Under General Models for IoT Data Collection
最小化物联网数据收集通用模型下的信息年龄
- DOI:
10.1109/tnse.2019.2952764 - 发表时间:
2020 - 期刊:
- 影响因子:6.6
- 作者:
Chengzhang Li;Shaoran Li;Yongce Chen;Thomas Hou;Wenjing Lou - 通讯作者:
Wenjing Lou
On the performance of MIMO-based ad hoc networks under imperfect CSI
不完善CSI下基于MIMO的自组织网络性能研究
- DOI:
10.1109/milcom.2008.4753523 - 发表时间:
2008 - 期刊:
- 影响因子:0
- 作者:
Jia Liu;Thomas Hou - 通讯作者:
Thomas Hou
Thomas Hou的其他文献
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{{ truncateString('Thomas Hou', 18)}}的其他基金
Analysis of Singularity Formation in Three-Dimensional Euler Equations and Search for Potential Singularities in Navier-Stokes Equations
三维欧拉方程奇异性形成分析及纳维-斯托克斯方程潜在奇异性搜索
- 批准号:
2205590 - 财政年份:2022
- 资助金额:
$ 31.38万 - 项目类别:
Continuing Grant
Solving Multiscale Problems and Data Classification with Subsampled Data by Integrating Partial Differential Equation Analysis with Data Science
通过将偏微分方程分析与数据科学相结合,利用二次采样数据解决多尺度问题和数据分类
- 批准号:
1912654 - 财政年份:2019
- 资助金额:
$ 31.38万 - 项目类别:
Standard Grant
A Computer-Assisted Analysis Framework for Studying Finite Time Singularities of the 3D Euler Equations and Related Models
用于研究 3D 欧拉方程及相关模型的有限时间奇异性的计算机辅助分析框架
- 批准号:
1907977 - 财政年份:2019
- 资助金额:
$ 31.38万 - 项目类别:
Standard Grant
NeTS: Small: Smart Interference Management for Wireless Internet of Things
NetS:小型:无线物联网的智能干扰管理
- 批准号:
1617634 - 财政年份:2016
- 资助金额:
$ 31.38万 - 项目类别:
Standard Grant
Investigating Potential Singularities in the Euler and Navier-Stokes Equations Using an Integrated Analytical and Computational Approach
使用综合分析和计算方法研究欧拉和纳维-斯托克斯方程中的潜在奇点
- 批准号:
1613861 - 财政年份:2016
- 资助金额:
$ 31.38万 - 项目类别:
Standard Grant
CPS: Synergy: Collaborative Research: Cognitive Green Building: A Holistic Cyber-Physical Analytic Paradigm for Energy Sustainability
CPS:协同:协作研究:认知绿色建筑:能源可持续性的整体网络物理分析范式
- 批准号:
1446478 - 财政年份:2015
- 资助金额:
$ 31.38万 - 项目类别:
Standard Grant
NeTS: JUNO: Cognitive Security: A New Approach to Securing Future Large Scale and Distributed Mobile Applications
NetS:JUNO:认知安全:保护未来大规模分布式移动应用程序的新方法
- 批准号:
1405747 - 财政年份:2014
- 资助金额:
$ 31.38万 - 项目类别:
Standard Grant
Data-Driven Time-Frequency Analysis via Nonlinear Optimization
通过非线性优化进行数据驱动的时频分析
- 批准号:
1318377 - 财政年份:2013
- 资助金额:
$ 31.38万 - 项目类别:
Standard Grant
FRG: Collaborative Research: Singularities, mixing and long time behavior in nonlinear evolution
FRG:协作研究:非线性演化中的奇异性、混合和长期行为
- 批准号:
1159138 - 财政年份:2012
- 资助金额:
$ 31.38万 - 项目类别:
Standard Grant
CSR: Small: Collaborative Research: Towards User Privacy in Outsourced Cloud Data Services
CSR:小型:协作研究:在外包云数据服务中实现用户隐私
- 批准号:
1217889 - 财政年份:2012
- 资助金额:
$ 31.38万 - 项目类别:
Standard Grant
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