Mathematical Sciences: Presidential Young Investigator Award

数学科学：总统青年研究员奖

• 批准号: 9057429
• 负责人: John Grove
• 金额: $ 23.75万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-15 至 1996-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9057429&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Presidential; Young; Investigator

The Presidential Young Investigator will conduct research in the area of computational fluid dynamics; in particular, he will study shock diffractions and bifurcations as different shocks interact with each other and with fluid interfaces and vortex sheets. This is very important and timely research, and it is of sufficient complexity that the PI will employ analytical methods from geometry and bifurcation theory, in addition to computational techniques. The goals of the research are twofold. The first goal is to discover different types of wave patterns that result from the complex interactions of shocks and fluid structures, while the second goal is to develop numerical methods that allow one to follow the evolution in time of the waves generated by the interactions. Many phenomena in fluid dynamics arise out of the interactions of different types of waves with each other and with internal fluid structures such as interfaces. What makes these interactions difficult to study mathematically is that they are described by systems of nonlinear differential equations, and so one must use computers in order to generate solutions. But this is tricky also, because computers can often generate meaningless information, unless the numerical methods used are reliable. The PI will study such problems with "intelligent" numerical methods. These are methods that have sufficient analytical and physical theory built into them that they produce sharp approximations to the correct physical solutions.

总统青年调查员将在 计算流体动力学领域;特别是，他将 研究激波绕射和分叉作为不同的激波 相互作用并与流体界面和涡流相互作用 薄膜. 这是一项非常重要和及时的研究， 足够的复杂性，PI将采用分析方法 从几何学和分叉理论，除了 计算技术 研究的目的是双重的。 第一个目标是发现不同类型的波型 这是由冲击和流体的复杂相互作用造成的 结构，而第二个目标是开发数值方法 可以让我们追踪海浪的演变 由互动产生。 流体动力学中的许多现象都是由 不同类型的波相互作用， 内部流体结构，如界面。 什么让这些 数学上难以研究的相互作用是， 由非线性微分方程系统描述， 必须使用计算机来生成解决方案。 但这 也很棘手，因为计算机通常可以生成毫无意义的 除非使用的数字方法是可靠的。 的 PI将用“智能”数值方法研究这些问题。 这些方法有足够的分析和物理 理论内置于他们，他们产生尖锐的近似， 正确的物理解决方案。