Development, Analysis and Applications for Numerical Methodsfor Nonlinear Partial Differential Equations

非线性偏微分方程数值方法的发展、分析与应用

• 批准号: 9103104
• 负责人: Stanley Osher
• 金额: $ 30万
• 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: 1991
• 资助国家: 美国
• 起止时间: 1991-07-15 至 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9103104&HistoricalAwards=false
• 关键词: Development; Analysis; Applications; Numerical; Methodsfor

Professors Osher, Engquist, and others will continue their individual and joint research on the development analysis and applications of numerical methods for nonlinear partial differential equations. Specific methods to be studied include: essentially nonoscillatory shock capturing techniques, front capturing algorithms, multiresolution and wavelet based methods, numerical homogenization, effective boundary conditions, kinetic models, spectral and viscosity methods, particle methods, and stochastic difference methods. Engineering and physical applications to be studied include: aerodynamical properties of high speed vehicles, hydrodynamic device models, miscible flow in porous media, combustion, reacting gas flows, shock turbulence interactions, microwave scattering, Boltzmann equations, nuclear fusion reactors, and core-annular flows. This broad range of activity has value both in its own right and with regard to extensive applications.

Osher、Engquist等教授将继续他们对非线性偏微分方程数值方法的发展、分析和应用的个人和联合研究。具体的研究方法包括：基本无振荡激波捕获技术、前沿捕获算法、多分辨率方法和基于小波的方法、数值均匀化、有效边界条件、动力学模型、谱和粘性方法、质点方法和随机差分方法。将研究的工程和物理应用包括：高速飞行器的空气动力学特性、流体动力装置模型、多孔介质中的混相流、燃烧、反应气体流动、激波湍流相互作用、微波散射、玻尔兹曼方程、核聚变反应堆和堆芯-环状流。这一广泛的活动本身和广泛的应用都具有价值。