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2010 Fiscal Year Final Research Report

Numerical and analytical studies on gas flows caused by the phase transition

Research Project

  • PDF
Project/Area Number 19560066
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Engineering fundamentals
Research InstitutionKyoto University

Principal Investigator

TAKATA Shigeru  Kyoto University, 大学院・工学研究科, 准教授 (60271011)

Project Period (FY) 2007 – 2010
Keywordsボルツマン方程式 / 相変化 / 膨張波 / 対称性 / 相反性
Research Abstract

We investigated the unsteady one-dimensional gas flows caused by a phase transition on the basis of the kinetic theory of gases. Main results are as follows. (1) Starting from the investigation of kinetic boundary-layer, we established a general theory of reciprocity for linearized problems. (2) We showed that from a certain class of initial states there occur two expansion waves traveling in the direction opposite to each other, which are separated by a highly rarefied region that evolves into a vacuum. This region is highly non-equilibrium and the temperature is strongly non-isotropic.

  • Research Products

    (15 results)

All 2010 2009 2008 Other

All Journal Article (6 results) (of which Peer Reviewed: 6 results) Presentation (9 results)

  • [Journal Article] Symmetry of the unsteady linearized Boltzmann equation in a fixed bounded domain2010

    • Author(s)
      S.Takata
    • Journal Title

      J.Stat.Phys. 140(5)

      Pages: 985-1005

    • Peer Reviewed
  • [Journal Article] Note on the relation between thermophoresis and slow uniform flow problems for a rarefied gas2009

    • Author(s)
      S.Takata
    • Journal Title

      Phys.Fluids 21(11),112001

      Pages: 7

    • Peer Reviewed
  • [Journal Article] Symmetry of the linearized Boltzmann equation II. Entropy production and Onsager-Casimir relation2009

    • Author(s)
      S.Takata
    • Journal Title

      J.Stat.Phys. 136(5)

      Pages: 945-983

    • Peer Reviewed
  • [Journal Article] Symmetry of the linearized Boltzmann equation and its application2009

    • Author(s)
      S.Takata
    • Journal Title

      J.Stat.Phys. 136(4)

      Pages: 751-784

    • Peer Reviewed
  • [Journal Article] On the long time behavior of gas flows by evaporation from a plane condensed phase2008

    • Author(s)
      S.Takata
    • Journal Title

      Bulletin of the Institute of Mathematics, Academia Sinica (New Series) 3(1)

      Pages: 115-147

    • Peer Reviewed
  • [Journal Article] Symmetry of the linearized Boltzmann equation

    • Author(s)
      S.Takata
    • Journal Title

      Proceedings of the 27th International Symposium on Rarefied Gas Dynamics 印刷中

    • Peer Reviewed
  • [Presentation] Symmetry of the linearized Boltzmann equation : A theory from steady to unsteady problem2010

    • Author(s)
      高田滋
    • Organizer
      International Conference on Nonlinear Partial Differential Equations : Mathematical Theory, Computation, and Applications
    • Place of Presentation
      Singapore (Singapore)
    • Year and Date
      20101129-20101203
  • [Presentation] On the symmetry of the linearized Boltzmann equation2010

    • Author(s)
      高田滋
    • Organizer
      The 27th International Symposium on Rarefied Gas Dynamics, Invited lecture of the session "Boltzmann and Related Equations," Pacific Grove
    • Place of Presentation
      California (USA)
    • Year and Date
      20100710-20100715
  • [Presentation] 定常系における線形化ボルツマン方程式の対称性について2010

    • Author(s)
      高田滋
    • Organizer
      日本航空宇宙学会関西支部第425回航空懇談会
    • Place of Presentation
      大阪大学工学研究科,吹田市
    • Year and Date
      2010-02-12
  • [Presentation] 分子気体力学における漸近解析-流体力学極限の理論とその周辺-2009

    • Author(s)
      高田滋
    • Organizer
      未来研究ラボ「非線形ダイナミクス」研究会「流体力学における漸近解析」
    • Place of Presentation
      大阪大学基礎工学研究科,吹田市
    • Year and Date
      20091201-20091202
  • [Presentation] Symmetry of the linearized Boltzmann equation and the Onsager-Casimir relation2009

    • Author(s)
      高田滋
    • Organizer
      2009 NIMS Hot Topics Workshop on Kinetic Theory and Fluid Dynamics
    • Place of Presentation
      Seoul National University, Seoul (Korea)
    • Year and Date
      20091022-20091024
  • [Presentation] Symmetry of the linearized Boltzmann equation, Modern Topics in Nonlinear Kinetic Equations2009

    • Author(s)
      高田滋
    • Organizer
      Department of Applied Mathematics and Theoretical Physics
    • Place of Presentation
      University of Cambridge, Cambridge (UK)
    • Year and Date
      20090420-20090422
  • [Presentation] Symmetry of the linearized Boltzmann equation2009

    • Author(s)
      高田滋
    • Organizer
      2009 Workshop on Kinetic Theory, Institute of Mathematics
    • Place of Presentation
      Academia Sinica, Taipei (Taiwan)
    • Year and Date
      20090321-20090323
  • [Presentation] 分子気体力学における解析と数値計算2009

    • Author(s)
      高田滋
    • Organizer
      CompView GCOE Symposium 「Workshop1 :偏微分方程式の理論と実践-流体解析を中心として
    • Place of Presentation
      東京工業大学,目黒区
    • Year and Date
      2009-12-03
  • [Presentation] 分子気体力学による流体力学極限の研究とその応用2008

    • Author(s)
      高田滋
    • Organizer
      2008年春季 第55回応用物理学関係連合講演会 日本真空協会企画シンポジウム「真空中の気体の流れ」
    • Place of Presentation
      日本大学理工学部 船橋キャンパス,船橋市
    • Year and Date
      2008-03-27

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Published: 2012-01-26   Modified: 2016-04-21  

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