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Study on the numerical analysis and its applications to engineering processes for free surface or interface flows

Research Project

Project/Area Number 15540113
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 InstitutionToyama University

Principal Investigator

OHMORI Katsushi  Toyama University, Faculty of Education, Professor, 教育学部, 教授 (20110231)

Co-Investigator(Kenkyū-buntansha) SAITO Norikazu  Toyama University, Faculty of Education, Associate Professor, 教育学部, 助教授 (00334706)
SAKURAGI Takuya  YKK Corporation, Research and Development Center, Manager, 研究開発センター, 解析室長
Project Period (FY) 2003 – 2004
Project Status Completed (Fiscal Year 2004)
Budget Amount *help
¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 2004: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2003: ¥2,400,000 (Direct Cost: ¥2,400,000)
Keywordstwo-fluid flows / Navier-Stokes equations / mass conservation / Lagrange multiplier technique / flux-free finite element method / Stokes interface problems / error estimates / convergence / Navier-Stokes方程式 / ラグランジュ未定乗数法 / 非圧縮性 / immiscible / フラックス汎関数 / ラグランジュ乗数 / 有限要素法
Research Abstract

This study has been carried out during 2003-2004 in order to develop and analyze the finite element scheme for free-surace or free interface flows and to consider its application to industrial processes.
In 2003, we have proposed the flux-free finite element method for two-fluid flows with free interface, which is based a new variational formulation including the flux-free constraint by using Lagrange multiplier technique. Then we have considered the mathematical validity of the new variational formulation of our problems, the uniqueness and existence of the stationary problem and the stability of the fractional projection scheme for Navier-Stokes equations. Furthermore we have performed many numerical experiments for dam-break problems and sloshing tank problems to demonstrate the efficiency of our method. As a result, our method shows the high quality for the mass conservation.
In 2004, we have also considered the convergence of the flux-free finite element method for two-fluid flows which is modelled by Navier-Stokes equations with discontinuous viscosity and density by using the arguments on the finite element aproximation for Stokes interface problems. In fact, we have proposed an error estimate of Strang type and have shown the convergence of the flux-free finite element method under the assumption on the smoothness of the interface and the regularity of the solution of Stokes interface problem.
However, so much remains to be considered about new finite element schemes for two-fluid flows with high ratios of the density and viscosity in the real application of our method to the mold filling simulations.

Report

(3 results)
  • 2004 Annual Research Report   Final Research Report Summary
  • 2003 Annual Research Report
  • Research Products

    (24 results)

All 2004 2003 Other

All Journal Article (17 results) Patent(Industrial Property Rights) (1 results) Publications (6 results)

  • [Journal Article] Benchmark problems for numerical schemes to passively transported interface2004

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

      International Journal of Computational Fluid Dynamics 18

      Pages: 317-322

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Mass conservative finite element method for free interface flows2004

    • Author(s)
      K.Ohmori, N.Saito, H.Okumura
    • Journal Title

      Proceedings of European Congress on Computational Methods in Applied Science and Engineering (ECCOMAS2004) II(CD-ROM)

      Pages: 1-13

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Remarks on the rational approximation of holomorphic semigroups with nonuniform partitions2004

    • Author(s)
      N.Saito
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics 21

      Pages: 323-337

    • NAID

      10018379799

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] A holomorphic semigroup approach to the lumped finite element method2004

    • Author(s)
      N.Saito
    • Journal Title

      Journal of Computational and Applied Mathematics 169

      Pages: 71-85

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Prediction of gas hole by molding filling simulation with consideration of surface tension2004

    • Author(s)
      T.Sakuragi
    • Journal Title

      Computational Fluid Dynamics Journal 47

      Pages: 699-708

    • NAID

      110004826638

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Annual Research Report 2004 Final Research Report Summary
  • [Journal Article] Benchmark problems for numerical schemes to passively transported interface2004

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

      International Journal of Computational Fluid Dynamics. Vol.18

      Pages: 317-322

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Mass conservative finite element method for free interface flows2004

    • Author(s)
      K.Ohmori, N.Saito, H.Okumura
    • Journal Title

      Proceedings of European Congress on Computational Methods in Applied Science and Engineering (ECCOMAS 2004) (P.Neittaanmaki et al.(eds)) Vol.II (CD-ROM)

      Pages: 1-13

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Remarks on the rational approximation of holomorphic semigroups with nonuniform partitions2004

    • Author(s)
      N.Saito
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics Vol.21, No.3

      Pages: 323-337

    • NAID

      10018379799

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] A holomorphic semigroup approach to the-lumped mass finite element method2004

    • Author(s)
      N.Saito
    • Journal Title

      Journal of Computational and Applied Mathematics Vol.169, No.1

      Pages: 71-85

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Prediction of gas hole by mold filling simulation with consideration of surface tension2004

    • Author(s)
      T.Sakuragi
    • Journal Title

      Computational Fluid Dynamics Journal, Special Issue Vol.47

      Pages: 699-708

    • NAID

      110004826638

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Benchmark problems for numerical schemes to passively transported interface2004

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

      International Journal of Comutational Fluid Dynamics 18・4

      Pages: 317-322

    • Related Report
      2004 Annual Research Report
  • [Journal Article] ラグランジュ乗数を用いた質量保存型有限要素法2004

    • Author(s)
      大森克史, 齊藤宣一
    • Journal Title

      計算工学講演会論文集 9

      Pages: 187-190

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Mass conservative finite element method for free interface flows2004

    • Author(s)
      K.Ohmori, N.Saito, H.Okumura
    • Journal Title

      Proceedings of European Congress on Comutational Methods in Applied Science and Engineering (ECCOMAS2004) II(CD-RON)

      Pages: 1-13

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Remarks on the rational approximation of holomorphic semigroups with nonuniform partitions2004

    • Author(s)
      N.Saito
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics 21・3

      Pages: 323-337

    • NAID

      10018379799

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A holomorphic semigroup approach to the lumped finite element method2004

    • Author(s)
      N.Saito
    • Journal Title

      Journal of Computational and Applied Mathematics 169・1

      Pages: 71-85

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Convergence analysis of the interface for interfacial transport phenomena2003

    • Author(s)
      K.Ohmori, S.Fujima, Y.Fujita
    • Journal Title

      Mathematics Journal of Toyama University 26

      Pages: 109-129

    • NAID

      110004679123

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Convergence analysis of the interface for interfacial transport phenomena2003

    • Author(s)
      K.Ohmori, S.Fujima, Y.Fujita
    • Journal Title

      Mathematics Journal of Toyama University Vol.26

      Pages: 109-129

    • NAID

      110004679123

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Patent(Industrial Property Rights)] 流動解析装置、流動解析方法、成型条件選択方法、鋳造製造方法、流動解析プログラム2004

    • Inventor(s)
      桜木 卓也
    • Industrial Property Rights Holder
      YKK(株)
    • Filing Date
      2004-03-02
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Publications] K.Ohmori, S.Fujima, Y.Fujita: "Convergence analysis of the interfacial transport phenomena"Math.J.Toyama Univ.. 26. 109-129 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 大森克史, 奥村弘: "ラグランジュ乗数を用いた質量保存型有限要素法による移動界面の解析"第17回数値流体力学シンポジウム講演論文集. (CD-ROM). 1-2 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Fajita, K.Ohmori: "A comparison theorem for Bellman equations of ergodic control"Differential and Integral Equations. 16. 641-651 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] S.Fujima, K.Ohmori: "Benchmark problems for numerical schemes to passively transported interface"Int.J.of Computational Fluid Dynamics. (to appear).

    • Related Report
      2003 Annual Research Report
  • [Publications] N.Saito, T.Suzuki: "A finite difference scheme to the system of self-interacting Particles"京都大学数理解析研究所講究録. 1320. 18-28 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] N.Saito: "A holomorphic semigroup approach to the lumped mass finite element method"J.Comput.Appi.Math.. (to appear).

    • Related Report
      2003 Annual Research Report

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Published: 2003-04-01   Modified: 2016-04-21  

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