U.S.-Brazil Cooperative Research: Analytical and Computational Methods Related to the Linearized Boltzmann Equation

这一美国-巴西奖项将支持北卡罗来纳州立大学的Charles E.Siewert博士与巴西阿雷格里港南里奥格兰德联邦大学的Liliane B.Barichello博士合作进行研究。他们的项目涉及稀薄气体动力学的一般领域，专注于解决Poiseuille流动问题、热蠕变流动问题和Couette流动问题，该问题由刚性球相互作用的线性化Boltzmann方程和在包含流动的两个表面上应用的Cercignani-Lampis边界条件定义。这项工作将基于解析离散纵坐标法，并使用勒让德展开的速度变量。这是一个重要的项目，其中PI考虑使用Cercignani-Lampis边界条件来定义平面通道中的Poiseuille流、热蠕变流和Couette流的经典问题。这项研究的结果可以帮助实现新的分析和计算方法，并将其应用于纳米技术，这是美国国家科学基金会和联邦政府的优先领域。再加上不断改进的计算机，它还有可能定义一个改进的机械系统分析和设计标准，正如PI与美国、巴西、日本和希腊的工程师就他们的工作进行的讨论所证明的那样。具体的可能应用包括微电子机械系统(MEMS)。

This U.S.-Brazil award will support Dr. Charles E. Siewert, North Carolina State University in a cooperative research effort with Dr. Liliane B. Barichello at Universidade Federal do Rio Grande do Sul in Porto Alegre, Brazil. Their project concerns the general area of rarefied-gas dynamics, focused on solving the Poiseuille-flow problem, the thermal-creep flow problem, and the Couette-flow problem as defined by the linearized Boltzmann equation for rigid-sphere interactions and the Cercignani-Lampis boundary condition applied at the two surfaces that contain flow. The work will be based on analytical discrete ordinates method and the use of a Legendre expansion in terms of the speed variable. This is an important project in which the PIs consider the use of the Cercignani-Lampis boundary condition to define the classical problems of Poiseuille flow, thermal-creep flow and Couette flow in plane channel.The results of this research could help implement new analytical and computational methods with applications to nanotechnology, a priority area for both NSF and the Federal Government. Coupled with ever-improved computing machines, it also has the potential to define an improved standard of analysis and design of mechanical systems, as evidenced by the PIs' discussions with engineers in the U.S., Brazil, Japan and Greece about their work. Specific possible applications include micro-electro-mechanical systems (MEMS).