Fast Spectral-Galerkin Methods and Their Applicatons

快速谱伽辽金方法及其应用

• 批准号: 0311915
• 负责人: Jie Shen
• 金额: $ 18.05万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-08-01 至 2007-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0311915&HistoricalAwards=false
• 关键词: Fast; Spectral; Galerkin; Methods; Their

The PI will develop and analyze fast and accurate spectral methodsfor solving a large class of partial differential equations and applythem to investigate several important problems of current interest,including in particular the inter-facial dynamics of multiphase complexflows, stability and dynamics of stratified shear flows andmicro-structural evolutions in advanced materials processing. Theproposed research will result in fast and accurate numericalalgorithms which will allow simulations of three-dimensionaltime-dependent problems within a reasonable turn-over time, andprovide capabilities to numerically attack challenging problemsarising from emerging engineering and scientific applications.As computer simulations are playing an ever increasing role in manybranches of science and engineering and are rapidly replacing much ofthe expensive prototyping and testing phases in manufacturing and inscience explorations, fast and robust numerical methods are becomingan indispensable tool for many scientists and engineers, especiallyfor computational scientists in fluid dynamics and materials science.It is expected that our numerical simulations will contribute towardsbetter understandings of the complex physical and mathematicalproblems, and provide valuable information for the designs of advancedmaterials and of a space experiment on stratified shear flows.

PI将开发和分析快速，准确的光谱方法，用于求解大量的部分微分方程，并应用以调查当前感兴趣的几个重要问题，包括尤其是多相络合物络合物的类型动力学，稳定性和分层剪切流的动力学，以及在高级材料处理中的微观结构发展。 该研究的研究将导致快速，准确的数值学位，这将允许在合理的转折时间内模拟三维时间依赖于时间的问题，并且可以在数值上攻击具有数值攻击的问题的能力，从而在新兴的工程和科学应用中逐渐攻击了挑战。对于许多科学家和工程师，尤其是流体动力学和材料科学领域的计算科学家，以及我们的数值模拟，我们的数值模拟将对复杂的物理和数学信息有助于对先进的实验和高级实验的设计，这将有助于对复杂的物理和数学信息，这是对快速的物理和数学信息的理解。