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Mathematical and physical study of moving boundary problems for the Boltzmann equation

Research Project

Project/Area Number 23360048
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Engineering fundamentals
Research InstitutionKyoto 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, 大学院工学研究科, 助教 (40335188)
NISHIBATA Shinya  東京工業大学, 大学院情報理工学研究科, 教授 (80279299)
Research Collaborator FILBET Francis  リヨン第1大学(フランス), 教授
GOLSE Francois  エコール・ポリテクニク(フランス), 教授
MARKOWICH Peter  ケンブリッジ大学(イギリス), 教授
PULVIRENTI Mario  ローマ第1大学(イタリア), 教授
VILLANI Cedric  アンリ・ポアンカレ研究所(フランス), 所長
Project Period (FY) 2011-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥20,670,000 (Direct Cost: ¥15,900,000、Indirect Cost: ¥4,770,000)
Fiscal Year 2013: ¥5,460,000 (Direct Cost: ¥4,200,000、Indirect Cost: ¥1,260,000)
Fiscal Year 2012: ¥5,460,000 (Direct Cost: ¥4,200,000、Indirect Cost: ¥1,260,000)
Fiscal Year 2011: ¥9,750,000 (Direct Cost: ¥7,500,000、Indirect Cost: ¥2,250,000)
Keywordsボルツマン方程式 / 移動境界問題 / クヌーセン層 / 希薄気体力学 / すべり境界条件
Research Abstract

The behavior of a gas in microscales and in low-pressure circumstances when the boundary is moving arbitrarily was investigated numerically on the basis of molecular gas dynamics. In particular, the singularities in the molecular velocity distribution function caused by the motion of the boundary were clarified, and a numerical method that is able to capture the singularities was constructed. The method was applied to various fundamental problems, such as the propagation of nonlinear acoustic waves and the decay of a pendulum in the gas.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • Research Products

    (53 results)

All 2014 2013 2012 2011 Other

All Journal Article (17 results) (of which Peer Reviewed: 14 results) Presentation (33 results) (of which Invited: 22 results) Remarks (3 results)

  • [Journal Article] Decay of a linear pendulum in a collisional gas : Spatially one-dimensional case2014

    • Author(s)
      T.Tsuji and K.Aoki
    • Journal Title

      Phys. Rev. E

      Volume: 89

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Gas motion in a microgap between a stationary plate and a plate oscillating in its normal direction2014

    • Author(s)
      T.Tsuji and K.Aoki
    • Journal Title

      Microfluid. Nanofluid.

      Volume: 16 (掲載予定) Issue: 6 Pages: 1033-1045

    • DOI

      10.1007/s10404-014-1374-2

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Moving boundary problems for a rarefied gas : Spatially one-dimensional case2013

    • Author(s)
      T.Tsuji and K.Aoki
    • Journal Title

      J. Comp. Phys.

      Volume: 250 Pages: 574-600

    • DOI

      10.1016/j.jcp.2013.05.017

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] 低圧気流の数値シミュレーション2013

    • Author(s)
      青木一生
    • Journal Title

      シミュレーション

      Volume: 32 Pages: 63-69

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Journal Article] 分子気体力学における移動境界問題の数値解析2013

    • Author(s)
      青木一生,辻徹郎
    • Journal Title

      ながれ

      Volume: 32 Pages: 233-238

    • NAID

      110009624787

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Journal Article] A simple model for flows around moving vanes in Crookes radiometer2012

    • Author(s)
      S.Taguchi and K.Aoki
    • Journal Title

      in 28th International Symposium on Rarefied Gas Dynamics 2012 (edited by M. Mareschal and A. Santos) (AIP, Melville)

      Volume: 1501 Pages: 786-793

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Numerical analysis of nonlinear acoustic wave propagation in a rarefied gas2012

    • Author(s)
      T.Tsuji and K.Aoki
    • Journal Title

      in 28th International Symposium on Rarefied Gas Dynamics 2012 (edited by M. Mareschal and A. Santos) (AIP, Melville)

      Volume: 1501 Pages: 115-122

    • NAID

      120005439716

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the second-order temperature jump coefficient of a dilute gas2012

    • Author(s)
      G.A.Radtke, N.G.Hadjiconstantinou, S.Takata, and K.Aoki
    • Journal Title

      J. Fluid Mech.

      Volume: 707 Pages: 331-341

    • Related Report
      2013 Final Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Parabolic temperature profile and second-order temperature jump of a slightly rarefied gas in an unsteady two-surface problem2012

    • Author(s)
      S.Takata, K.Aoki, M.Hattori, and N.G.Hadjiconstantinou
    • Journal Title

      Phys. Fluid

      Volume: 24

    • NAID

      120004920388

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Decay of a linear pendulum in a free-molecular gas and in a special Lorentz gas2012

    • Author(s)
      T.Tsuji and K.Aoki
    • Journal Title

      J. Stat. Phys.

      Volume: 146 Pages: 620-645

    • NAID

      120003874276

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Numerical analysis of nonlinear acoustic wave propagation in a rarefied gas2012

    • Author(s)
      T. Tsuji, K. Aoki
    • Journal Title

      The Proceedings of 28th International Symposium on Rarefied Gas Dynamics 2012, AIP Conf. Proc.

      Volume: 1501 Pages: 115-122

    • DOI

      10.1063/1.4769485

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A simple model for flows around moving vanes in Crookes radiometer2012

    • Author(s)
      S. Taguchi
    • Journal Title

      28th International Symposium on Rarefied Gas Dynamics 2012: AIP Conf. Proc.

      Volume: 1501 Pages: 786-793

    • DOI

      10.1063/1.4769622

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 温度場によって誘起される低圧気流の数値解析2012

    • Author(s)
      青木一生
    • Journal Title

      ながれ

      Volume: 31 Pages: 105-110

    • NAID

      110009445179

    • Related Report
      2012 Annual Research Report
  • [Journal Article] Decay of a linear pendulum in a free-molecular gas and in a special Lorentz gas2012

    • Author(s)
      T.Tsuji, K.Aoki
    • Journal Title

      J.Stat.Phys.

      Volume: 146 Issue: 3 Pages: 620-645

    • DOI

      10.1007/s10955-011-0412-7

    • NAID

      120003874276

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Parabolic temperature profile and second-order temperature jump of a slightly rarefied gas in an unsteady two-surface problem2012

    • Author(s)
      S.Takata, K.Aoki, M.Hattori, N.G.Hadjiconstantinou
    • Journal Title

      Phys.Fluids

      Volume: 24 Issue: 3 Pages: 32002-32002

    • DOI

      10.1063/1.3691262

    • NAID

      120004920388

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stagnation-point flow of a rarefied gas impinging obliquely on a plane wall2011

    • Author(s)
      K.Aoki and Y.Abe
    • Journal Title

      Kinetic Related Models

      Volume: 4 Pages: 935-954

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stagnation-point flow of a rarefied gas impinging obliquely on a plane wall2011

    • Author(s)
      K.Aoki, Y.Abe
    • Journal Title

      Kinetic and Related Models

      Volume: 4 Issue: 4 Pages: 935-954

    • DOI

      10.3934/krm.2011.4.935

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Presentation] Decay of a linear pendulum in a collisional gas : Spatially one-dimensional case2014

    • Author(s)
      K.Aoki
    • Organizer
      6th International Workshop on Kinetic Theory & Applications
    • Place of Presentation
      Karlstad University, Karlstad, Sweden
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Some recent topics in classical kinetic theory of gases2013

    • Author(s)
      K.Aoki
    • Organizer
      Tullio Levi-Civita Lectures, Dipartimento di Matematica Guido Castelnuovo
    • Place of Presentation
      Universita di Roma "La Sapienza", Roma, Italy
    • Year and Date
      2013-10-16
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Rarefied gas flows between two coaxial rotating cylinders at small Knudsen numbers : DSMC and slip flow theory (Graeme A. Bird Keynote Lecture)2013

    • Author(s)
      K.Aoki
    • Organizer
      Direct Simulation Monte Carlo 2013 : Theory, Methods and Applications
    • Place of Presentation
      Santa Fe, USA
    • Related Report
      2013 Final Research Report
  • [Presentation] Decay of a linear pendulum in a rarefied gas2013

    • Author(s)
      K.Aoki
    • Organizer
      The 2nd Pacific Rim Mathematical Association Congress
    • Place of Presentation
      Shanghai Jiao Tong University, Shanghai, China
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Some moving boundary problems in kinetic theory of gases : Spatially one-dimensional problems2013

    • Author(s)
      K.Aoki
    • Organizer
      The 17th International Conference on Waves and Stability in Continuous Media
    • Place of Presentation
      Levico Terme (Trento), Italy
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Moving boundary problems for a rarefied gas : Spatially one-dimensional case2013

    • Author(s)
      K.Aoki
    • Organizer
      Workshop : Issues in Solving the Boltzmann Equation for Aerospace Applications, Institute for Computational and Experimental Research in Mathematics
    • Place of Presentation
      Brown University, Providence, USA
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Moving boundary problems in kinetic theory of gases (Plenary Lecture)2013

    • Author(s)
      K.Aoki
    • Organizer
      The 8th International Conference on Computational Physics
    • Place of Presentation
      Hong Kong Baptist University, Hong Kong
    • Related Report
      2013 Final Research Report
  • [Presentation] Moving boundary problems for a rarefied gas: Spatially one-dimensional case2013

    • Author(s)
      K. Aoki
    • Organizer
      Workshop: Issues in Solving the Boltzmann Equation for Aerospace Applications
    • Place of Presentation
      Providence (USA)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Some moving boundary problems in kinetic theory of gases: Spatially one-dimensional problems2013

    • Author(s)
      K. Aoki
    • Organizer
      The 17th International Conference on Waves and Stability in Continuous Media (WASCOM)
    • Place of Presentation
      Levico Terme (Italy)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Decay of a linear pendulum in a rarefied gas2013

    • Author(s)
      K. Aoki
    • Organizer
      The 2nd Pacific Rim Mathematical Association Congress
    • Place of Presentation
      Shanghai (China)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Numerical analysis of moving boundary problems in rarefied gas dynamics2013

    • Author(s)
      T. Tsuji and K. Aoki
    • Organizer
      RIMS Workshop: Mathematical Analysis in Fluid and Gas Dynamics
    • Place of Presentation
      Kyoto (Japan)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 希薄気体力学における移動境界問題2013

    • Author(s)
      辻 徹郎,青木一生
    • Organizer
      日本流体力学会年会講演会2013
    • Place of Presentation
      東京
    • Related Report
      2013 Annual Research Report
  • [Presentation] Some recent topics in classical kinetic theory of gases2013

    • Author(s)
      K. Aoki
    • Organizer
      Levi-Civita Lectures
    • Place of Presentation
      Rome (Italy)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Rarefied gas flows between two coaxial rotating cylinders at small Knudsen numbers: DSMC and slip flow theory2013

    • Author(s)
      K. Aoki
    • Organizer
      Direct Simulation Monte Carlo 2013: Theory, Methods and Applications
    • Place of Presentation
      Santa Fe (USA)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Moving boundary problems in kinetic theory of gases2013

    • Author(s)
      K. Aoki
    • Organizer
      8th International Conference on Computational Physics
    • Place of Presentation
      Hong Kong
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Moving boundary problems in kinetic theory of gases2012

    • Author(s)
      K.Aoki
    • Organizer
      Convegno Internazionale : La geometria degli atomi e delle molecole. La Meccanica negli studi di Carlo Cercignani
    • Place of Presentation
      Istituto Lombardo, Milano, Italy
    • Year and Date
      2012-11-22
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Kinetic theory approach to microscale gas flows (Plenary Lecture)2012

    • Author(s)
      K.Aoki
    • Organizer
      The 3rd European Conference on Microfluidics
    • Place of Presentation
      Heidelberg, Germany
    • Related Report
      2013 Final Research Report
  • [Presentation] Singular and moving boundary problems in kinetic theory. Part 1 : Singular boundary, Part 2: Moving boundary2012

    • Author(s)
      K.Aoki
    • Organizer
      Summer School : Methods and Models of Kinetic Theory
    • Place of Presentation
      Porto Ercole, Grosseto, Italy
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Decay of a linear pendulum in a rarefied gas2012

    • Author(s)
      K.Aoki
    • Organizer
      Spring School : Kinetic Theory and Fluid Mechanics
    • Place of Presentation
      Universite Claude Bernard (Lyon 1), Lyon, France
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Singular and moving boundary problems in kinetic theory. Part 1: Singular boundary, Part 2: Moving boundary2012

    • Author(s)
      K. Aoki
    • Organizer
      Summer School: Methods and Models of Kinetic Theory
    • Place of Presentation
      Porto Ercole (Italy)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Numerical analysis of nonlinear acoustic wave propagation in a rarefied gas2012

    • Author(s)
      T. Tsuji
    • Organizer
      28th International Symposium on Rarefied Gas Dynamics
    • Place of Presentation
      Zaragoza (Spain)
    • Related Report
      2012 Annual Research Report
  • [Presentation] A simple model for flows around moving vanes in Crookes radiometer2012

    • Author(s)
      S. Taguchi
    • Organizer
      28th International Symposium on Rarefied Gas Dynamics
    • Place of Presentation
      Zaragoza (Spain)
    • Related Report
      2012 Annual Research Report
  • [Presentation] Numerical analysis of moving boundary problems in kinetic theory2012

    • Author(s)
      T Tsuji
    • Organizer
      Workshop on Kinetic Theory and Related Fields: Theoretical and Numerical Approaches
    • Place of Presentation
      Kyoto
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Moving boundary problems in kinetic theory of gases2012

    • Author(s)
      K. Aoki
    • Organizer
      Convegno Internazionale: La geometria degli atomi e delle molecole. La Meccanica negli studi di Carlo Cercignani
    • Place of Presentation
      Milano (Italy)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Kinetic theory approach to microscale gas flows2012

    • Author(s)
      K. Aoki
    • Organizer
      3rd European Conference on Microfluidics
    • Place of Presentation
      Heidelberg (Germany)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Asymptotic analysis for boundary-value problems of the Boltzmann equation (120min)2011

    • Author(s)
      K.Aoki
    • Organizer
      Tutorial Talk at ICERM
    • Place of Presentation
      Brown Univ.(USA)
    • Year and Date
      2011-11-04
    • Related Report
      2011 Annual Research Report
  • [Presentation] Some considerations on radiometric effects2011

    • Author(s)
      K.Aoki
    • Organizer
      Workshop : Novel Applications of Kinetic Theory and Computations, Institute for Computational and Experimental Research in Mathematics
    • Place of Presentation
      Brown University, Providence, USA
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Some considerations on radiometric effect2011

    • Author(s)
      K.Aoki
    • Organizer
      Non Linear Hyperbolic Systems of Balance Laws in Extended Thermodynamics and Kinetic Theory
    • Place of Presentation
      Cortona, Italy
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Moving boundary problems in collisionless kinetic theory2011

    • Author(s)
      K.Aoki
    • Organizer
      The 8th International Conference for Mesoscopic Methods in Engineering and Science, Institut National des Sciences Appliquees de Lyon
    • Place of Presentation
      Lyon, France
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Decay of an oscillating disk in a collision-less gas : A long-memory effect (40min)2011

    • Author(s)
      K.Aoki
    • Organizer
      The 2011 Annual Kinetic FRG Meeting : Kinetic Description of Multiscale Phenomena
    • Place of Presentation
      University of Wisconsin-Madison (USA)
    • Related Report
      2011 Annual Research Report
  • [Presentation] Decay of an oscillating disk in a gas : Case of a collision-less gas and a special Lorentz gas (50min)2011

    • Author(s)
      K.Aoki
    • Organizer
      Conference on Kinetic Theory and Related Fields
    • Place of Presentation
      Pohang Univ.of Science and Technology (Korea)
    • Related Report
      2011 Annual Research Report
  • [Presentation] Moving boundary problems in collisionless kinetic theory (40min)2011

    • Author(s)
      K.Aoki
    • Organizer
      8th International Conference for Mesoscopic Methods in Engineering and Science
    • Place of Presentation
      INSA de Lyon (France)
    • Related Report
      2011 Annual Research Report
  • [Presentation] Asymptotic methods for rarefied gas flows based on the Boltzmann equation (90min×3)2011

    • Author(s)
      K.Aoki
    • Organizer
      Lecture Series at Mechanical Engineering
    • Place of Presentation
      MIT (USA)
    • Related Report
      2011 Annual Research Report
  • [Remarks]

    • URL

      http://www.mfd.me.kyoto-u.ac.jp/member/aoki/aokij.htm

    • Related Report
      2013 Final Research Report
  • [Remarks] 青木一生

    • URL

      http://www.mfd.me.kyoto-u.ac.jp/member/aoki/aokij.htm

    • Related Report
      2013 Annual Research Report
  • [Remarks]

    • URL

      http://www.mfd.me.kyoto-u.ac.jp/member/aoki/aokij.htm

    • Related Report
      2011 Annual Research Report

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Published: 2011-04-06   Modified: 2019-07-29  

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