Mathematical Sciences: Numerical Solution of Stiff Ordinary Differential Equations and the Navier-Stokes Equation

数学科学：刚性常微分方程和纳维-斯托克斯方程的数值解

• 批准号: 8719952
• 负责人: Heinz Kreiss
• 金额: $ 22.71万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-05-01 至 1991-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8719952&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Numerical; Solution; Stiff

This research lies in the areas of numerical analysis and the mathematical theory of fluid dynamics. Part of the work will examine stiff systems of ordinary differential equations on a bounded interval. Such equations arise in the study of nearly inviscid fluid flow problems, semiconductor physics, and reaction-diffusion phenomena. Numerical methods to solve these nonlinear equations will be developed based on continuation and linearization. The incompressible Navier-Stokes equations in two space dimensions will also be considered. Results will be tested at the level of the smallest scales. This resolution is needed in flow problems with high Reynolds numbers. Results of this work will be immediately relevant to the numerical simulation of homogeneous turbulence. They will also lead to the development of better algorithms for fluid flow problems and increased physical insight into the mechanisms of stability and transition.

这项研究属于数值分析和流体动力学数学理论领域。 部分工作将检查有界区间上的常微分方程的刚性系统。 此类方程出现在近无粘性流体流动问题、半导体物理和反应扩散现象的研究中。 求解这些非线性方程的数值方法将基于延拓和线性化而发展。 二维空间中不可压缩的纳维-斯托克斯方程也将被考虑。 结果将在最小尺度的水平上进行测试。 对于高雷诺数的流动问题需要这种解决方案。 这项工作的结果将直接与均匀湍流的数值模拟相关。 它们还将导致开发更好的流体流动问题算法，并增加对稳定性和转变机制的物理洞察力。