Mathematical and physical study of micro- and nano-scale gas flows on the basis of the Boltzmann equation

基于玻尔兹曼方程的微纳尺度气体流动的数学和物理研究

• 批准号: 20360046
• 负责人: AOKI Kazuo
• 金额: $ 11.73万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20360046/
• 关键词: ボルツマン方程式; 気体分子運動論; マイクロ流体力学; 移流拡散モデル; 応用数学

Diffusion-type equations that describe gas flows through a micro-nano channel with a width much shorter than the length was derived on the basis of molecular gas dynamics by a systematic asymptotic analysis. With the help of the derived equations, the properties of gas flows (in particular, gas flows through a twisty channel) were clarified. In addition, a direct numerical method based on molecular gas dynamics was constructed for wider micro channels.

基于分子气体动力学，通过系统渐近分析，推导出描述气体流经宽度远小于长度的微纳通道的扩散型方程。借助推导出来的方程，阐明了气流（特别是通过弯曲通道的气流）的特性。此外，针对更宽的微通道构建了基于分子气体动力学的直接数值方法。

项目成果

Fluid models and simulations of internal rarefied gasflows (mini-course, 90min×5times)

内部稀薄气流的流体模型与模拟（迷你课程，90min×5次）

• 发表时间: 2008
• 作者: K. Aoki;S. Takata
• 通讯作者: S. Takata

Poiseuille flow and thermal transpiration of a rarefied polyatomic gas through a circular tube with applications to microflows

稀薄多原子气体通过圆管的泊肃叶流和热蒸腾及其在微流中的应用

• 发表时间: 2011
• 期刊: Bollettino dell'Unione Matematica Italiana, Ser.9 4
• 作者: H.Funagane;S.Takata;K.Aoki;K.Kugimoto
• 通讯作者: K.Kugimoto

Some considerations on collisionless gases (Invited Lecture)

关于无碰撞气体的一些思考（特邀报告）

• 发表时间: 2009
• 作者: M.Saka;K.Sasagawa;M.Muraoka;H.Tohmyoh;Y.Ju;K.Aoki
• 通讯作者: K.Aoki

Asymptotic behavior of solutions to the Euler-Poisson equation in plasma physics (45min)

等离子体物理学中欧拉-泊松方程解的渐近行为（45 分钟）

• 发表时间: 2010
• 作者: 作田康裕;佐藤明;松永怜也;徳悠葵,村岡幹夫;S.Nishibata
• 通讯作者: S.Nishibata

Shock structure analysis in chemically reacting gas mixtures by a relaxation-time kinetic model

• DOI: 10.1063/1.3013637
• 发表时间: 2008-11
• 期刊: Physics of Fluids
• 影响因子: 4.6
• 作者: M. Groppi;K. Aoki;G. Spiga;V. Tritsch