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Development and analysis of new numerical methods for two-fluid problems

Research Project

Project/Area Number 22540143
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

TABATA Masahisa  早稲田大学, 理工学術院, 教授 (30093272)

Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords応用数学 / モデル化 / 二流体問題 / 数値解析 / 特性曲線有限要素法 / 有限要素法 / 表面張力 / エネルギー安定性 / 特性曲線 / ナヴィエ・ストークス方程式 / 分離・併合 / 集中質量近似
Research Abstract

A new numerical scheme has been developed for two-fluid problems such as gas-liquid two-phase flows, where multiple fluids coexist. This scheme is based on the mathematical theory established in the single-fluid problem, is applicable to problems in the domain of any shape and subject to the force at the interface of fluids, and has the advantage of low computation cost since the resultant linear system is symmetric. Simulating the movement of two fluids with different densities in a container of hourglass shape by this scheme, we have realized numerically the phenomena of splitting and merging of fluids.

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (49 results)

All 2013 2012 2011 2010 Other

All Journal Article (17 results) (of which Peer Reviewed: 9 results) Presentation (25 results) (of which Invited: 1 results) Book (4 results) Remarks (3 results)

  • [Journal Article] Behavior of finite element solutions subject to strong-type Robin conditions2013

    • Author(s)
      M. Tabata
    • Journal Title

      COE Lecture Note (Institute of Mathematics for Industry, Kyushu Univ)

      Volume: Vol. 45 Pages: 1-15

    • Related Report
      2012 Final Research Report
  • [Journal Article] Behavior of finite element solutions subject to strong-type Robin conditions2013

    • Author(s)
      M. Tabata
    • Journal Title

      COE Lecture Note, Institute of Mathematics for Industry, Kyushu Univ.

      Volume: 45 Pages: 1-15

    • Related Report
      2012 Annual Research Report
  • [Journal Article] 非格子点関数値を要する有限差分近似2012

    • Author(s)
      田端正久, 野津裕史
    • Journal Title

      日本応用数理学会論文誌

      Volume: Vol. 22 Pages: 171-179

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Quadrature-free characteristic methods for convection-diffusion problems2012

    • Author(s)
      M. Tabata
    • Journal Title

      Proceedings of the Eighth International Conference on Engineering Computational Technology, B. H. V. Topping (editor, Civil-Comp Press, Stirlingshire, Scotlan)

      Pages: 1801-1812

    • Related Report
      2012 Final Research Report
  • [Journal Article] 非格子点関数値を要する有限差分近似2012

    • Author(s)
      田端正久
    • Journal Title

      日本応用数理学会 論文誌

      Volume: 22 Pages: 171-179

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] ガレルキン・特性曲線有限要素法-理論と応用2012

    • Author(s)
      田端正久
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1791 Pages: 76-86

    • Related Report
      2011 Annual Research Report
  • [Journal Article] 特性曲線有限差分法の離散L2理論2012

    • Author(s)
      野津裕史, 田端正久
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1791 Pages: 151-157

    • Related Report
      2011 Annual Research Report
  • [Journal Article] Proceedings of the Eighth International Conference on Engineering Computational Stability and convergence of a Galerkin-characteristics finite element scheme of lumped mass type2010

    • Author(s)
      O. Pironneau and M. Tabata.
    • Journal Title

      International Journal for Numerical Methods in Fluids

      Volume: Vol. 64 Pages: 1240-1253

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Numerical simulation of fluid movement in an hourglass by an energy-stable finite element scheme2010

    • Author(s)
      M. Tabata
    • Journal Title

      Computational Fluid Dynamics Review 2010 (In M. N. Hafez, K. Oshima, and D. Kwak, editors, World Scientific, Singapore)

      Pages: 29-50

    • Related Report
      2012 Final Research Report
  • [Journal Article] Finite element computation for scattering problems of micro-hologram using DtN map2010

    • Author(s)
      Y. Mizuyama, T. Shinde, M. Tabata, and D. Tagami
    • Journal Title

      JSIAM Letters

      Volume: Vol. 2 Pages: 45-48

    • NAID

      130000257641

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Amass-conservative characteristic finite element scheme for convection-diffusion problems2010

    • Author(s)
      H. Rui and M. Tabata
    • Journal Title

      Journal of Scientific Computing

      Volume: Vol. 43 Pages: 416-432

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stability and convergence of a Galerkin-characteristics finite element scheme of lumped mass type2010

    • Author(s)
      O.Pironneau, M.Tabata
    • Journal Title

      International Journal for Numerical Methods in Fluids

      Volume: 64 Pages: 1240-1253

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Numerical simulation of fluid movement in an hourglass by an energy-stable finite element scheme2010

    • Author(s)
      M.Tabata
    • Journal Title

      In M.N.Hafez, K.Oshima, and D.Kwak, editors, Computational Fluid Dynamics Review 2010, World Scientific, Singapore

      Pages: 20-50

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Finite element computation for scattering problems of micro-hologram using DtN map2010

    • Author(s)
      Y.Mizuyama, T.Shinde, M.Tabata, D.Tagami.
    • Journal Title

      JSIAM Letters

      Volume: 2 Pages: 45-48

    • NAID

      130000257641

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A mass-conservative characteristic finite element scheme for convection-diffusion problems2010

    • Author(s)
      H.Rui, M.Tabata
    • Journal Title

      Journal of Scientific Computing

      Volume: 43 Pages: 416-432

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Finite element matrices in congruent subdomains and some techniques for practical problems2010

    • Author(s)
      A.Suzuki, M.Tabata
    • Journal Title

      In F.Magoules, editor, Domain Decomposition Methods : Algorithma and Practice, Civil-Comp Press, Edinburgh

      Pages: 229-266

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Development and L2-analysis of a single-step characteristics finite difference scheme of second order in time for convection-diffusion problems

    • Author(s)
      H. Notsu, H. Rui, and M. Tabata
    • Journal Title

      Journal of Algorithms and Computational Technology

      Volume: (掲載決定)

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Presentation] Quadrature-free characteristic methods for convection-diffusion problems2012

    • Author(s)
      M.Tabata
    • Organizer
      The 8th International Conference on Engineering Computational Technology
    • Place of Presentation
      Hotel Dubrovnik Palace, Dubrovnik, Croatia
    • Year and Date
      2012-09-05
    • Related Report
      2012 Annual Research Report 2012 Final Research Report
  • [Presentation] Galerkin-characteristics finite element methods - theory and applications2012

    • Author(s)
      M. Tabata
    • Organizer
      Workshop on Modeling, optimization and simulation of complex fluid flow
    • Place of Presentation
      Technische Universitat Darmstadt, Darmstadt, Germany
    • Year and Date
      2012-06-20
    • Related Report
      2012 Final Research Report
  • [Presentation] Quadrature-free characteristics methods for convection-diffusion terms, International Workshop on Computational Science and Numerical Analysis2012

    • Author(s)
      M. Tabata
    • Organizer
      The University of Electro-Communications
    • Place of Presentation
      Chofu, Tokyo
    • Year and Date
      2012-03-24
    • Related Report
      2012 Final Research Report
  • [Presentation] Numerical simulations of two-fluid flow problems by a Galerkincharacteristics finite element scheme2012

    • Author(s)
      M. Tabata
    • Organizer
      5th International Conference on High Performance Scientific Computing - Modelling, Simulation and Optimization of Complex Processes, Institute of Mathematics
    • Place of Presentation
      Vietnam Academy of Science and Technology, Hanoi, Vietnam
    • Year and Date
      2012-03-09
    • Related Report
      2012 Final Research Report
  • [Presentation] Numerical simulations of two-fluid flow problems by a Galerkin-characteristics finite element scheme2012

    • Author(s)
      田端正久
    • Organizer
      5th International Conference on High Performance Scientific Computing
    • Place of Presentation
      ハノイ(ベトナム)
    • Year and Date
      2012-03-09
    • Related Report
      2011 Annual Research Report
  • [Presentation] Galerkin-characteristics finite element methods for flow problems2011

    • Author(s)
      M. Tabata
    • Organizer
      1st International Conference on Numerical Analysis & Optimization - Theory and Applications
    • Place of Presentation
      King Fahd University of Petroleum & Minerals, Dhahran, Kingdom of Saudi Arabia
    • Year and Date
      2011-12-18
    • Related Report
      2012 Final Research Report
  • [Presentation] Galerkin-characteristics finite element methods for flow problems2011

    • Author(s)
      田端正久
    • Organizer
      1st International Conferrence on Numerical Analysis and Optimization-Theory and Applications
    • Place of Presentation
      ダンマン(サウジアラビア)(招待講演)
    • Year and Date
      2011-12-18
    • Related Report
      2011 Annual Research Report
  • [Presentation] 数値シミュレーションへの誘い2011

    • Author(s)
      田端正久
    • Organizer
      日本数学会2011 年度秋季総合分科会市民講演会
    • Place of Presentation
      松本中央公民館, 松本
    • Year and Date
      2011-10-01
    • Related Report
      2012 Final Research Report
  • [Presentation] 数値シミュレーションへの誘い2011

    • Author(s)
      田端正久
    • Organizer
      日本数学会2011年度秋季総合分科会市民講演会
    • Place of Presentation
      松本中央公民館(長野県)(招待講演)
    • Year and Date
      2011-10-01
    • Related Report
      2011 Annual Research Report
  • [Presentation] 離散L2評価と特性曲線法2011

    • Author(s)
      野津裕史
    • Organizer
      日本応用数理学会2011年度年会
    • Place of Presentation
      同志社大学今出川キャンパス(京都府)
    • Year and Date
      2011-09-14
    • Related Report
      2011 Annual Research Report
  • [Presentation] Galerkin-characteristics finite element approximation and its application to two-fluid flow problems2011

    • Author(s)
      M. Tabata
    • Organizer
      7th International Congress on Industrial and Applied Mathematics
    • Place of Presentation
      Vancouver Convention Centre, Vancouver, Canada
    • Year and Date
      2011-07-20
    • Related Report
      2012 Final Research Report
  • [Presentation] Galerkin-characteristics finite element approximation and its application to two-fluid flow problems2011

    • Author(s)
      田端正久
    • Organizer
      7th International Congress on Industrial and Applied Mathematies
    • Place of Presentation
      バンクーバー(カナダ)
    • Year and Date
      2011-07-20
    • Related Report
      2011 Annual Research Report
  • [Presentation] 圧力安定化特性曲線有限要素スキームによる熱対流問題の数値シミュレーション2011

    • Author(s)
      野津裕史
    • Organizer
      第16回計算工学講演会
    • Place of Presentation
      東京大学柏キャンパス(千葉県)
    • Year and Date
      2011-05-25
    • Related Report
      2011 Annual Research Report
  • [Presentation] Energy-stable Galerkincharacteristics finite element approximation to two-fluid flow problems2011

    • Author(s)
      M. Tabata
    • Organizer
      16th International Conference on Finite Elements in Flow Problems
    • Place of Presentation
      Munick, Germany
    • Year and Date
      2011-03-23
    • Related Report
      2012 Final Research Report
  • [Presentation] Energy-stable Galerkin-characteristics finite element approximation to two-fluid flow problems2011

    • Author(s)
      M.Tabata
    • Organizer
      16th International Conference on Finite Elements in Flow Problems
    • Place of Presentation
      Munich, Germany
    • Year and Date
      2011-03-23
    • Related Report
      2010 Annual Research Report
  • [Presentation] 多流体問題のためのエネルギー安定特性曲線有限要素法2010

    • Author(s)
      田端正久
    • Organizer
      第24回数値流体力学シンポジウム
    • Place of Presentation
      横浜
    • Year and Date
      2010-12-21
    • Related Report
      2010 Annual Research Report
  • [Presentation] エネルギー安定性を満たすスキームの作成とその応用2010

    • Author(s)
      田端正久
    • Organizer
      日本数学会2010年度秋季総合分科会
    • Place of Presentation
      名古屋
    • Year and Date
      2010-09-24
    • Related Report
      2010 Annual Research Report
  • [Presentation] 質量保存性と特性有限要素近似II2010

    • Author(s)
      田端正久, Hongxing Rui
    • Organizer
      日本応用数理学会2010年度年会
    • Place of Presentation
      東京
    • Year and Date
      2010-09-06
    • Related Report
      2010 Annual Research Report
  • [Presentation] Finite element characteristic methods for two-fluid flow problems2010

    • Author(s)
      M. Tabata
    • Organizer
      The 3rd China-Japan-Korea Joint Conference on Numerical Mathematics
    • Place of Presentation
      Gangneung-Wonju National University, Korea
    • Year and Date
      2010-08-19
    • Related Report
      2012 Final Research Report
  • [Presentation] Finite element characteristic methods for two-fluid flow problems2010

    • Author(s)
      M.Tabata
    • Organizer
      The 3rd China-Japan-Korea Joint Conference on Numerical Mathematics
    • Place of Presentation
      Gangneung, Korea(招待講演)
    • Year and Date
      2010-08-19
    • Related Report
      2010 Annual Research Report
  • [Presentation] Energy-stable Galerkincharacteristics finite element approximation to multi-fluid flow problems2010

    • Author(s)
      M. Tabata
    • Organizer
      The 6th International Conferenc on Computational Fluid Dynamics
    • Place of Presentation
      St. Petersburg, Russia
    • Year and Date
      2010-07-14
    • Related Report
      2012 Final Research Report
  • [Presentation] 風上有限要素法と特性曲線有限要素法の同等性

    • Author(s)
      田端正久
    • Organizer
      日本数学会2013年度年会
    • Place of Presentation
      京都大学吉田キャンパス, 京都
    • Related Report
      2012 Annual Research Report
  • [Presentation] 特性曲線差分スキームと離散 L2 理論

    • Author(s)
      野津裕史
    • Organizer
      特性曲線差分スキームと離散 L2 理論
    • Place of Presentation
      国立オリンピック記念青少年総合センター, 東京
    • Related Report
      2012 Annual Research Report
  • [Presentation] Oseen方程式のための圧力安定化特性曲線有限要素スキームの誤差評価

    • Author(s)
      野津裕史
    • Organizer
      日本数学会2012年度秋季総合分科会
    • Place of Presentation
      九州大学伊都キャンパス, 福岡
    • Related Report
      2012 Annual Research Report
  • [Presentation] Galerkin-characteristics finite element methods -- theory and applications

    • Author(s)
      M. Tabata
    • Organizer
      Workshop on Modeling, optimization and simulation of complex fluid flow
    • Place of Presentation
      Technische Universität Darmstadt, Darmstadt, Germany
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Book] 応用数理ハンドブック2013

    • Author(s)
      田端正久(分担執筆)
    • Total Pages
      8
    • Publisher
      コロナ社
    • Related Report
      2012 Annual Research Report
  • [Book] Domain Decomposition Methods: Algorithms and Practice (F. Magoules, editor の Chapter 9: Finite element matrices in congruent subdomains and some techniques for practical problems を執筆)2010

    • Author(s)
      A. Suzuki and M. Tabata
    • Publisher
      Civil-Comp Press, Edinburgh,
    • Related Report
      2012 Final Research Report
  • [Book] 偏微分方程式の数値解析2010

    • Author(s)
      田端正久
    • Total Pages
      144
    • Publisher
      岩波書店
    • Related Report
      2012 Final Research Report 2010 Annual Research Report
  • [Book] 応用数理ハンドブック

    • Author(s)
      田端正久(薩摩順吉, 大石進一, 杉原正顕(編))
    • Total Pages
      8
    • Publisher
      朝倉書店 (印刷中)
    • Related Report
      2012 Final Research Report
  • [Remarks] 見出し : 来月1日,松本で日本数学会講演会長野. 平成23年9月26日付け長野MSN 産経ニュース

    • Related Report
      2012 Final Research Report
  • [Remarks] 記事内容 : 日本数学会2011 年度秋季総合分科会の市民講演会が松本市の中央公民館で開催され,早稲田大学理工学術院の田端正久氏が「数値シミュレーションへの誘い」と題して講演する. 平成23 年9 月26 日付け長野MSN 産経ニュース

    • Related Report
      2012 Final Research Report
  • [Remarks]

    • URL

      https://www.wnp7.waseda.jp/Rdb/app/ip/ipi0211.html?lang_kbn=0&kensaku_no=5716

    • Related Report
      2010 Annual Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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