Nonlinear slip boundary conditions for the compressible Navier-Stokes equations

2015 Fiscal Year Final Research Report

• Project/Area Number: 26630051
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Fluid engineering
• Research Institution: Kyoto University
• Principal Investigator: Aoki Kazuo 京都大学, 工学(系)研究科(研究院), 教授 (10115777)
• Co-Investigator(Kenkyū-buntansha): KOSUGE Shingo 京都大学, 工学研究科, 助教 (40335188)
• Project Period (FY): 2014-04-01 – 2016-03-31
• Keywords: ボルツマン方程式 / ナヴィエ‐ストークス方程式 / すべり境界条件 / 希薄気体力学 / 非平衡気体 / 気体分子運動論

Outline of Final Research Achievements

The correct slip boundary conditions for the compressible Navier-Stokes equations were derived in a mathematically systematic way on the basis of the Boltzmann equation, so that the fluid-dynamic system that replaces the Boltzmann system under wide conditions has been established. This facilitates the treatment of the nonlinear phenomena in low-pressure gases and gases in microscales with small Knudsen numbers. On the basis of this system, some basic problems, such as the propagation of nonlinear acoustic waves in a rarefied gas, the formation of stationary waves in a rarefied gas between two plates, the decay of the oscillation of a plate in a gas subjecting to a restoring force, have been analyzed numerically over a long time, and some peculiar phenomena have been clarified.

Free Research Field

分子気体力学