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教授，Engquist和其他人将继续他们的个人和共同研究在非线性偏微分方程中数值方法的开发分析和应用。 要研究的特定方法包括：基本上是非振荡性冲击捕获技术，前捕获算法，基于多分辨率和小波的方法，数值均匀化，有效的边界条件，动力学模型，光谱和粘度方法，粒子方法，粒子方法和随机差异方法。 要研究的工程和物理应用包括：高速车辆的空气动力学特性，流体动力设备模型，多孔培养基中的可混杂流动，燃烧，反应气流，电击湍流相互作用，微波散射，玻尔兹曼方程，核融合反应堆，核融合反应堆和核心空间。 这项广泛的活动本身具有价值，并且在广泛的应用方面具有价值。