Symbolic Computing and Dimensionally Reduced Models of Fluid Flow

流体流动的符号计算和降维模型

• 批准号: 9531828
• 负责人: Stanly Steinberg
• 金额: $ 4.18万
• 依托单位: University of New Mexico
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-06-15 至 2000-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9531828&HistoricalAwards=false
• 关键词: Symbolic; Computing; Dimensionally; Reduced; Models

This project will develop new methods for numerically modelling incompressible fluid flows of the type that appear in global environmental modelling problems. The proposed models are hyperbolic and dispersive vertically-averaged models of stratified incompressible flow which are derived from the Navier-Stokes equations. These models reduce three-dimensional models to a system of complex two-dimensional models, which promise greater numerical efficiency. However, the averaged models are not well posed for some interesting ranges of their parameters. Consequently, their instability and regularization must be investigated. This analysis, along with the discretization of the continuum equations, the accuracy and stability analysis of the discrete problems, and the coding of the discrete equations are all algebraically complex, so the use of computer algebra will play a critical role in this project. The results of the project can be used for the global modelling of the ocean, the atmosphere, and other complex environments. The current codes implementing detailed models of such environments require computational resources that tax even the largest computers. The goal of this project is to produce new models and numerical methods for their solution which would represent a significant improvement in efficiency and accuracy over existing models for some important applications. ***

这个项目将开发新的方法来数值模拟不可压缩流体流动的类型出现在全球环境模拟问题。本文提出的分层不可压缩流模型是由Navier-Stokes方程导出的双曲型和色散型垂直平均模型。这些模型将三维模型简化为复杂的二维模型系统，从而保证了更高的数值效率。然而，平均模型在一些有趣的参数范围内不能很好地定位。因此，必须研究它们的不稳定性和正则化。这个分析，随着连续统方程的离散化，离散问题的精度和稳定性分析，离散方程的编码都是代数复杂的，因此使用计算机代数将在这个项目中发挥关键作用。该项目的结果可用于海洋、大气和其他复杂环境的全球模拟。目前实现这种环境的详细模型的代码需要计算资源，甚至是最大的计算机。该项目的目标是为其解决方案提供新的模型和数值方法，这将在某些重要应用中比现有模型的效率和准确性有重大改进。＊＊＊