Mathematical Sciences: Analytical Problems for Models in Compressible Fluid Mechanics

数学科学：可压缩流体力学模型的分析问题

• 批准号: 9623037
• 负责人: Irene Gamba
• 金额: $ 5.35万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-01 至 1999-09-27
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9623037&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Analytical; Problems; Models

9623037 Gamba This proposal concerns problems that model potential compressible fluid flow and charged-particle transport systems. The compressible fluid flow models under consideration include the standard transonic flow problem in gas dynamics, its viscous approximations and boundary value problem, and the Mach reflection problem when a weak shock (pressure) wave collides with an oblique obstacle. Models of charged- particle transport systems are studied within the framework of submicron electronic devices. In particular these models include electro- hydrodynamic or energy-transport models for semiconductors, related models for plasmas, boundary value problems and their high field approximations. %%% Areas of applications of the proposed research include models in aerodynamics and aircraft design. In particular, wing performance just below supersonic speeds and wing design for flight in the upper atmosphere. These are models that describe how a gas moves around an object at high speeds (i.e. close to producing sonic booms). In addition models of ionized plasmas and electron transport are considered. In particular, the design and performance simulation of semiconductor devices of extremely small size and even quantum level. The models under consideration describe the flow of current in the working of a submicron or a quantum-scale electronic device. The core of the proposal focuses on issues related to questions of validity and stability of models based on the available data. This information is of paramount importance in finding the best computational strategy for the computer aided simulation of experiments. ***

小行星9623037 这个建议涉及的问题，模型潜在的可压缩 流体流动和带电粒子传输系统。可压缩流体 正在考虑的流动模型包括标准 跨音速流 气体动力学中的一个问题，它的粘性近似和 边界 价值问题，以及马赫反射问题时， 弱势震荡 （压力）波与倾斜障碍物碰撞。充电模式- 粒子输运系统是在亚微米 电子设备。具体而言，这些模型包括 电的，电的 半导体的流体动力学或能量输运模型， 等离子体模型、边值问题及其高场 近似值 %%% 拟议研究的应用领域包括以下模型： 空气动力学和飞机设计。 特别是，Wing 性能略低于超音速和机翼设计的飞行 在高层大气中。这些模型描述了气体 以高速围绕物体移动（即接近产生音爆）。 此外，电离等离子体和电子输运模型被认为是。 特别是半导体器件的设计和性能模拟 非常小的尺寸甚至是量子级别的设备。模型 在考虑描述电流的流动在工作中的一个 亚微米或量子级电子器件。提案的核心 重点关注与有效性问题有关的问题， 模型稳定性 根据现有的数据。这一信息在以下方面至关重要： 找到 最佳计算策略 模拟实验。 ***