Mathematical Sciences: Time-Discretization Schemes for Incompressible Navier-Stokes Equations and Burgers' Equation

数学科学：不可压缩纳维-斯托克斯方程和伯格斯方程的时间离散方案

• 批准号: 8701109
• 负责人: Tunc Geveci
• 金额: $ 8.59万
• 依托单位: San Diego State University Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1989-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701109&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Time; Discretization; Schemes

This research program is concerned with the stability, accuracy and effectiveness of fully discrete schemes which result from the application of certain time-differencing schemes to semidiscrete versions of the Navier-Stokes equations describing incompressible flow and Burgers' equation. The emphasis is on semidiscrete approximations which are derived via the Galerkin method. The analysis part of the research will clarify the essential features that admissible numerical solution schemes should possess. The algorithms developed will enable scientists and engineers to solve many technical problems in incompressible fluid flow which cannot be solved by current techniques.

这项研究计划关注的是稳定性， 精度和有效性的全离散计划， 由于应用了一定的时间差 纳维尔-斯托克斯方程半离散版本的方案 描述不可压缩流和Burgers方程。 的 重点是半离散近似， 通过Galerkin方法。 分析部分的研究将阐明本质 特征，容许数值解方案应 拥有. 开发的算法将使科学家和 工程师解决了不可压缩的许多技术问题， 流体流动，这是当前技术无法解决的问题。