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Development of a nonreflecting boundary condition based on the Riemann invariant manifold

Research Project

Project/Area Number 19760051
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Engineering fundamentals
Research InstitutionThe University of Tokyo

Principal Investigator

YAGUCHI Takaharu  The University of Tokyo, 大学院・情報工学系研究科, 助教 (10396822)

Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥3,940,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥540,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,600,000 (Direct Cost: ¥1,600,000)
Keywords数理工学 / 無反射境界条件 / Riemann不変量多様体 / 圧縮流体 / 計算物理 / 離散変分法 / 人工的境界条件 / Euler方程式 / 計算空力音響学
Research Abstract

Nonreflecting boundary conditions are of importance in numerical simulations of compressive fluid. In this research I developed a new nonreflecting boundary condition based on the Riemann invariant manifold. An improvement of this boundary condition was found to be same as Thompson's boundary condition, and this provided a new derivation of Thompson's boundary condition and a stability analysis. Researches on the discrete variational method are also performed in order to stabilize this boundary condition. As a result, some extensions of the discrete variational method are achieved.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (32 results)

All 2010 2009 2008 2007 Other

All Journal Article (9 results) (of which Peer Reviewed: 5 results) Presentation (23 results)

  • [Journal Article] Conservative Numerical Schemes for the Ostrovsky Equation2010

    • Author(s)
      T. Yaguchi, T. Matsuo, M. Sugihara
    • Journal Title

      J. Comput. Appl. Math. 234

      Pages: 1036-1048

    • Related Report
      2009 Final Research Report
  • [Journal Article] An Extension of the Discrete Variational Method to Nonuniform Grids2010

    • Author(s)
      T. Yaguchi, T. Matsuo, M. Sugihara
    • Journal Title

      J. Comput. Phys. 229

      Pages: 4382-4423

    • Related Report
      2009 Final Research Report
  • [Journal Article] Conservative Numerical Schemes for the Ostrovsky Equation2010

    • Author(s)
      谷口隆晴, 松尾宇泰, 杉原正顯
    • Journal Title

      Journal of Computational and Applied Mathematics 234

      Pages: 1036-1048

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An Extension of the Discrete Variational Method to Nonuniform Grids2010

    • Author(s)
      谷口隆晴, 松尾宇泰, 杉原正顯
    • Journal Title

      Journal of Computational Physics 229

      Pages: 4382-4423

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 離散変分法の非一様格子への拡張2009

    • Author(s)
      谷口隆晴, 松尾宇泰, 杉原正顯
    • Journal Title

      応用数理学会論文誌 19

      Pages: 371-431

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] 離散変分法の非一様格子への拡張2009

    • Author(s)
      谷口隆晴, 松尾宇泰, 杉原正顯
    • Journal Title

      日本応用数理学会論文誌 19

      Pages: 371-431

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 非粘性圧縮流体の等エントロピー流れにおけるある人工的境界条件とそのThompsonの無反射境界条件との関係について2008

    • Author(s)
      谷口隆晴
    • Journal Title

      応用数理学会論文誌 18

      Pages: 447-471

    • Related Report
      2009 Final Research Report 2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 波動現象シミュレーションのための無反射境界の作り方2007

    • Author(s)
      谷口隆晴
    • Journal Title

      シミュレーション 26

      Pages: 84-89

    • NAID

      110006368726

    • Related Report
      2009 Final Research Report
  • [Journal Article] 波動現象シミューレーションのための無反射境界の作り方2007

    • Author(s)
      谷口 隆晴
    • Journal Title

      シミュレーション 26

      Pages: 84-89

    • NAID

      110006368726

    • Related Report
      2007 Annual Research Report
  • [Presentation] Symmetry-Based Method to Derive Conservative Numerical Schemes for the Euler-Lagrange PDEs2010

    • Author(s)
      谷口隆晴
    • Organizer
      2010 Tokyo Workshop on Structure-Preserving Methods
    • Place of Presentation
      東京
    • Year and Date
      2010-03-23
    • Related Report
      2009 Annual Research Report
  • [Presentation] Euler-Lagrange 偏微分方程式に対する対称性を用いた保存スキームの導出法2010

    • Author(s)
      谷口隆晴, 松尾宇泰, 杉原正顯
    • Organizer
      日本応用数理学会研究部会連合発表会
    • Place of Presentation
      茨城
    • Year and Date
      2010-03-09
    • Related Report
      2009 Annual Research Report
  • [Presentation] 非線形Klein-Gordon方程式に対する対称性を用いた保存スキームの導出法2009

    • Author(s)
      谷口隆晴, 松尾宇泰, 杉原正顯
    • Organizer
      応用数学合同研究集会
    • Place of Presentation
      滋賀
    • Year and Date
      2009-12-17
    • Related Report
      2009 Annual Research Report
  • [Presentation] ハミルトン偏微分方程式に対する解析力学的空間離散化法とその応用2009

    • Author(s)
      谷口隆晴, 松尾宇泰, 杉原正顯
    • Organizer
      RIMS研究集会「数値解析と数値計算アルゴリズムの最近の展開」
    • Place of Presentation
      京都
    • Year and Date
      2009-12-15
    • Related Report
      2009 Annual Research Report
  • [Presentation] 離散変分法の幾何学的再定式化2009

    • Author(s)
      谷口隆晴, 松尾宇泰, 杉原正顯
    • Organizer
      日本応用数理学会2009年度年会
    • Place of Presentation
      大阪
    • Year and Date
      2009-09-28
    • Related Report
      2009 Annual Research Report
  • [Presentation] An Energy Conservative Numerical Scheme on Mixed Meshes for the Nonlinear Schrodinger Equation2009

    • Author(s)
      T. Yaguchi, T. Matsuo, M. Sugihara
    • Organizer
      7th International Conference of Numerical Analysis and Applied Mathematics
    • Place of Presentation
      Crete, Greece
    • Year and Date
      2009-09-19
    • Related Report
      2009 Final Research Report
  • [Presentation] An Energy Conservative Numerical Scheme on Mixed Meshes for the Nonlinear Schrodinger Equation2009

    • Author(s)
      谷口隆晴, 松尾宇泰, 杉原正顯
    • Organizer
      7th International Conference of Numerical Analysis and Applied Mathematics(ICNAAM 2009)
    • Place of Presentation
      ギリシャ, レシムノ
    • Year and Date
      2009-09-19
    • Related Report
      2009 Annual Research Report
  • [Presentation] An Extension of the Discrete Variational Derivative Method to Nonuniform Meshes2009

    • Author(s)
      谷口隆晴, 松尾宇泰, 杉原正顯
    • Organizer
      2009 International Conference on Scientific Computation and Differential Equations(SciCADE09)
    • Place of Presentation
      中国, 北京
    • Year and Date
      2009-05-29
    • Related Report
      2009 Annual Research Report
  • [Presentation] Challenge for Multi-Dimensional Cases II: on Non-Uniform Meshes2009

    • Author(s)
      T. Yaguchi
    • Organizer
      Workshop on Structure-Preserving Methods for Partial Differential Equations
    • Place of Presentation
      Tokyo, Japan
    • Year and Date
      2009-03-17
    • Related Report
      2009 Final Research Report
  • [Presentation] Challenge for Multi-Dimensional Cases II : on Non Uniform Meshes2009

    • Author(s)
      T. Yaguchi
    • Organizer
      Workshop on Structure-Preserving Methods for Partial Differential Equations
    • Place of Presentation
      東京
    • Year and Date
      2009-03-17
    • Related Report
      2008 Annual Research Report
  • [Presentation] An Extension of the Discrete Variational Derivative Method to Mixed Meshes by the2009

    • Author(s)
      T. Yaguchi, T. Matsuo and M. Sugihara
    • Organizer
      SIAM Conference on Computational Science and Engineering (CSE09)
    • Place of Presentation
      アメリカ, マイアミ
    • Year and Date
      2009-03-04
    • Related Report
      2008 Annual Research Report
  • [Presentation] 離散外微分形式を用いた離散変分法の拡張2008

    • Author(s)
      谷口隆晴, 松尾宇泰, 杉原正顯
    • Organizer
      応用数学合同研究集会
    • Place of Presentation
      瀬田
    • Year and Date
      2008-12-17
    • Related Report
      2008 Annual Research Report
  • [Presentation] Conservative Finite Difference Schemes for the Ostrovsky Equation2008

    • Author(s)
      T. Yaguchi, T. Matsuo and M. Sugihara
    • Organizer
      International Symposium on Frontiers of Computational Science 2008
    • Place of Presentation
      名古屋
    • Year and Date
      2008-11-29
    • Related Report
      2008 Annual Research Report
  • [Presentation] 複素保存型偏微分方程式に対する混合メッシュ上のエネルギー保存スキーム2008

    • Author(s)
      谷口隆晴, 松尾宇泰, 杉原正顯
    • Organizer
      日本応用数理学会2008年度年会
    • Place of Presentation
      千葉
    • Year and Date
      2008-09-19
    • Related Report
      2008 Annual Research Report
  • [Presentation] The Discrete Variational Derivative Method for a Class of Equations with Nonlocal Conservation/Dissipation Properties2008

    • Author(s)
      T. Yaguchi, T. Matsuo, M. Sugihar
    • Organizer
      13th International Congress on Computational and Applied Mathematics
    • Place of Presentation
      Ghent, Belgium
    • Year and Date
      2008-07-10
    • Related Report
      2009 Final Research Report
  • [Presentation] The Discrete Variational Derivative Method for a Class of Equations with Nonlocal Conservation/Dissipation Properties2008

    • Author(s)
      T. Yaguchi, T. Matsuo and M. Sugihara
    • Organizer
      13th International Congress on Computational and Applied Mathematics
    • Place of Presentation
      ベルギー, ゲント
    • Year and Date
      2008-07-10
    • Related Report
      2008 Annual Research Report
  • [Presentation] Ostrovsky方程式に対する保存スキーム2008

    • Author(s)
      谷口隆晴, 松尾宇泰, 杉原正顯
    • Organizer
      第37回数値解析シンポジウム
    • Place of Presentation
      秋田
    • Year and Date
      2008-06-14
    • Related Report
      2008 Annual Research Report
  • [Presentation] 等エントロピー流れにおけるRiemann不変量多様体を用いた無反射境界条件について2008

    • Author(s)
      谷口隆晴
    • Organizer
      日本応用数理学会2008年研 究部会連合発表会
    • Place of Presentation
      東京
    • Year and Date
      2008-03-08
    • Related Report
      2009 Final Research Report
  • [Presentation] 等エントロピー流れにおけるRiemann不変量多様体を用いた無反射境界条件について2008

    • Author(s)
      谷口 隆晴
    • Organizer
      日本応用数理学会2007年度研究部会連合発表会
    • Place of Presentation
      首都大学東京
    • Year and Date
      2008-03-08
    • Related Report
      2007 Annual Research Report
  • [Presentation] 多次元準線形双曲型偏微分方程式系に対する無反射境界条件2007

    • Author(s)
      谷口隆晴
    • Organizer
      日本応用数理学会 2007年度年会
    • Place of Presentation
      北海道大学
    • Year and Date
      2007-09-17
    • Related Report
      2007 Annual Research Report
  • [Presentation] Characteristic non-reflecting boundary conditions for multi-dimensional quasi-linear hyperbolic systems2007

    • Author(s)
      T. Yaguchi
    • Organizer
      6th International Congress on. Industrial and Applied Mathematics
    • Place of Presentation
      Zurich, Switzerland
    • Year and Date
      2007-07-16
    • Related Report
      2009 Final Research Report
  • [Presentation] Characteristic Nonreflecting Boundary Conditions for Multidimensional Quasi-Linear Hyperbolic Systems2007

    • Author(s)
      Takaharu Yaguchi
    • Organizer
      6th International Congress on Industrial and Applied Mathematics
    • Place of Presentation
      ETH Zurich
    • Year and Date
      2007-07-16
    • Related Report
      2007 Annual Research Report
  • [Presentation] Symmetry-Based Method to Derive Conservative Numerical Schemes for the Euler-Lagrange PDEs

    • Author(s)
      T. Yaguchi
    • Organizer
      2010 Tokyo Workshop on Structure-Preserving Methods
    • Place of Presentation
      Tokyo, Japan
    • Related Report
      2009 Final Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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