Mathematical Sciences: Analytical Problems for Models in Compressible Fluid Mechanics

这个建议涉及到模拟潜在的可压缩流体流动和带电粒子输运系统的问题。考虑的可压缩流体流动模型包括气体动力学中的标准跨音速流动问题、其粘性近似和边值问题以及弱激波（压力）波与斜障碍物碰撞时的马赫反射问题。在亚微米电子器件的框架内研究了带电粒子输运系统的模型。特别是这些模型包括半导体的电流体动力学或能量输运模型、等离子体的相关模型、边值问题及其高场近似。所提出的研究的应用领域包括空气动力学模型和飞机设计。特别是，机翼性能刚好低于超音速和机翼设计在高层大气中飞行。这些模型描述了气体如何在物体周围高速运动（即接近产生音爆）。此外，还考虑了电离等离子体和电子输运的模型。特别是极小尺寸甚至量子级半导体器件的设计与性能模拟。所考虑的模型描述了亚微米级或量子级电子设备工作时的电流流动。该提案的核心是关于基于现有数据的模型的有效性和稳定性问题。这些信息对于寻找计算机辅助实验模拟的最佳计算策略至关重要。＊＊＊

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. ***