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2009 Fiscal Year Final Research Report

Mathematical studies on fluid motions under certain conditions

Research Project

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Project/Area Number 18340030
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionHiroshima University

Principal Investigator

NAKAKI Tatsuyuki  Hiroshima University, 大学院・理学研究科, 教授 (50172284)

Co-Investigator(Kenkyū-buntansha) OHMORI Katsushi  富山大学, 人間発達科学部, 教授 (20110231)
TSUJIKAWA Tohru  宮崎大学, 工学部, 教授 (10258288)
FUKUMOTO Yasuhide  九州大学, 大学院・数理学研究院, 教授 (30192727)
HATTORI Yuji  東北大学, 流体科学研究所, 教授 (70261469)
SAKAJO Takashi  北海道大学, 大学院・理学研究院, 教授 (10303603)
KIMURA Masato  九州大学, 大学院・理学研究院, 准教授 (70263358)
Project Period (FY) 2006 – 2009
Keywords流体 / 数学解析 / 数値解析 / 渦運動 / 多孔質媒体流 / 緩和振動 / 不安定性 / 自由境界問題
Research Abstract

The fluid motion was studied from mathematical and numerical points of view. We focused our attention on the following cases :
(1) Point vortex problems : Our studies are made under some assumptions on the strength and initial position of vortices.
(2) Problems of vortex ring and so on : By the theoretical analysis, we studied the instability of vortices.
(3) 1 or 2 phase-flow problems : The numerical schemes for the computer simulations were developed and studied. Our interests were the conservative schemes, and natural and effective determination of interfaces.

  • Research Products

    (12 results)

All 2009 2008 2007

All Journal Article (6 results) (of which Peer Reviewed: 6 results) Presentation (5 results) Book (1 results)

  • [Journal Article] ある拡散現象における解のサポートの反復した分離・融合について2009

    • Author(s)
      友枝謙二, 中木達幸
    • Journal Title

      日本応用数理学会論文誌 第19巻

      Pages: 25~37

    • Peer Reviewed
  • [Journal Article] Short-wavelength stability analysis of a helical vortex tube2009

    • Author(s)
      Y. Hattori, Y. Fukumoto
    • Journal Title

      Physics of Fluid 第21巻

      Pages: 014104, 7

    • Peer Reviewed
  • [Journal Article] From generation to chaotic motion of a ring configuration of vortex structures on a sphere2009

    • Author(s)
      T. Sakajo
    • Journal Title

      Theoretical and Computational Fluid Dynamics

    • URL

      doi:10.1007/s00162-009-0116-7

    • Peer Reviewed
  • [Journal Article] Second order numerical scheme for motion of polygonal curves with constant area speed2009

    • Author(s)
      M. Benes, M. Kimura, S. Yazaki
    • Journal Title

      Interfaces and Free Boundaries 第11巻

      Pages: 515~536

    • Peer Reviewed
  • [Journal Article] Interfacial analysis to a chemotaxis model equation with growth in three dimension2007

    • Author(s)
      T. Tsujikawa
    • Journal Title

      Advanced Studies in Pure Mathematics 第47巻

      Pages: 785~805

    • Peer Reviewed
  • [Journal Article] Flux-free finite element method with Lagrange multipliers for two-fluid flows2007

    • Author(s)
      K. Ohmori, S. Saito
    • Journal Title

      Journal of Scientific Computing 第32巻

      Pages: 147~173

    • Peer Reviewed
  • [Presentation] A singular limit method of two immiscible fluids in porous media2009

    • Author(s)
      T. Nakaki
    • Organizer
      Algoritmy 2009: Conference on Scientific Computing
    • Place of Presentation
      Hotel PERMON, Podbanske(スロバキア)
    • Year and Date
      2009-03-19
  • [Presentation] Stationary solutions of shadow system for an adsorbate-induced phase transition model2008

    • Author(s)
      T. Tsujikawa
    • Organizer
      研究集会「自己相似構造と自己組織化に関する漸近解析」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2008-09-18
  • [Presentation] Curvature Instability of a vortex ring and a helical vortex tube2008

    • Author(s)
      Y. Fukumoto
    • Organizer
      XXII International Congress of Theoretical and Applied Mechanics (ICTAM)
    • Place of Presentation
      Adelaide Convention Center, Adelaide(オーストラリア)
    • Year and Date
      2008-08-26
  • [Presentation] Flux-free finite element method for immiscible two-fluid flows2008

    • Author(s)
      K. Ohmori
    • Organizer
      5th European Congress on Computational Methods in Applied Sciences and Engineering
    • Place of Presentation
      Venice(イタリア)
    • Year and Date
      2008-07-01
  • [Presentation] Numerical Detection of a New Instability Mode of a Vortex Ring, FEDSM 20052007

    • Author(s)
      Y. Hattori
    • Organizer
      5th Joint ASME/JSME Fluids Engineering Conference
    • Place of Presentation
      Sheraton San Diego Hotel, San Diego(アメリカ)
    • Year and Date
      2007-08-01
  • [Book] 技術に生きる現代数学, 第5章「渦を破壊せよ」2008

    • Author(s)
      福本康秀
    • Total Pages
      206,133~174
    • Publisher
      岩波書店

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Published: 2011-06-18   Modified: 2016-04-21  

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