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Study on the finite element method for fluid flows with moving boundary

Research Project

Project/Area Number 12640110
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 InstitutionUniversity of Toyama

Principal Investigator

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

Co-Investigator(Kenkyū-buntansha) FUJITA Yasuhiro  Toyama University, Faculty of Science, Associate Professor, 理学部, 助教授 (10209067)
IKEDA Hideo  Toyama University, Faculty of Science, Professor, 理学部, 教授 (60115128)
Project Period (FY) 2000 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2002: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2001: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2000: ¥2,200,000 (Direct Cost: ¥2,200,000)
KeywordsTwo-fluid flows / Incompressible / Immiscible / Finite element method / Convergence of interface / Mass conservation / 擬密度関数
Research Abstract

This study has been carried out during 2000-2002 in order to develop and analyze the finite element method for fluid flows with moving boundary, which are often appeared in nature and some industrial processes.
In 2000, we have considered the convergence of the approximate interface in the finite element approximation for the incompressible immiscible two-fluid flows. We have estimated the L^p (Ω)norm of the difference between the measure of the positive value of the pseudo-density function and its approximation by using the Heaviside operator H(・). Due to our result, the convergence rate is O(h^<2k/3p>) in the case of P_k-finite element. This result has been tested by numerical experiments.
In 2001, we have improved the previous result by means of the regularized Heaviside operator. Then the convergence rate of the approximate interface measured by the L^2(Ω)-norm is O(h^<1/2>) in the case of P_1 or P_1isoP_2-element. This result is also tested by some numerical experiments.
In 2003, we have considered the mass conservative finite element scheme for incompressible immiscible two-fluid flows. We have proposed the mixed variational formulation with the flux functional for Navier-Stokes equations. We have proved the existence and the uniqueness for continuous and approximate problems, however, the application to the non-stationary problem and the numerical computation are our theme in the near future.

Report

(4 results)
  • 2002 Annual Research Report   Final Research Report Summary
  • 2001 Annual Research Report
  • 2000 Annual Research Report
  • Research Products

    (18 results)

All Other

All Publications (18 results)

  • [Publications] K.Ohmori: "Convergence of the interface in the finite element approximation for two-fluid flows"Lecture Notes in Pure and Applied Mathematics. 223. 279-291 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S.Fujima, K.Ohmori: "Finite element analysis using a regularized Heaviside function for interfacial transport phenomena"Proceedings of Computational Engineering Conference. 7. 757-758 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S.Fujima, K.Ohmori: "Benchmark problems for numerical schemes to passively transported interface"Computational Fluid Dynamics Journal. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H.Ikeda, M.Mimura, H.Okamoto: "A singular perturbation problem arising in Oseen's spiral flows"Japan Journal of Industrial and Applied Mathematics. 18. 393-403 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y.Fujita, K.Ohmori: "A comparison theorem Bellman equations of ergodic control"Differential and Integral Equations. 16(to appear). (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] OHMORI, Katsushi: "Convergence of the interface in the finite element approximation for two-fluid flows"Lecture Notes in Pure and Applied Mathematics. 223. 279-291 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] FUJIMA, Shoichi and OHMORI, Katsushi: "Finite element analysis using a regularized Heaviside function for interfacial transport phenomena"Proceedings of Computational Engineering Conference. 7. 757-758 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] FUJIMA, Sshoichi and OHMORI, Katsushi: "Benchmark problems for numerical schemes to passively transported interface"to appear in Computational Fluid Dynamics Journal.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] IKEDA, Hideo, MIMURA, Masayasu and OKAMOTO, Hisashi: "A singular problem arising in Oseen's spiral flows"Japan Journal of Industrial and Applied Mathematics. 18. 393-403 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] FUJIMA, Yasuhiro and OHMORI, Katsushi: "A comparison theorem for Bellman equations of ergodic control"Differential and Integral Equations (to appear). 16. (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S.Fujima, K.Ohmori: "Finite element analysis using a regularized Heaviside function for interfacial transport phenomena"Proceedings of Computational Engineering Conference. 7. 757-758 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] S.Fujima, K.Ohmori: "Benchmark problems for numerical schemes to passively transported interface"Computational Fluid Dynamics Journal. (to appear).

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Fujita, K.Ohmori: "A comparison theorem for Bellman equations of ergodic control"Differential and Integral Equations. 16(to appear). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Ohmori: "Convergence of the interface in the finite clement approximation for two-fluid flows"Lecture Note in Pure and Applied Mathematics. 223. 279-293 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] H.Ikeda, M.Mimura, H.Okamoto: "A singular perturbation problem arising in Oseen's spiral flows"Japan J. Indust Appl. Math. 18. 393-403 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Y.Fujita: "An auxiliary equation for the Bellman equations in a one-dimensional ergodic control"Applied Mathematics and Optimization. 43. 169-186 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] K.Ohmori: "Convergence of the interface in the finite element approximation for two-fluid flows"Navier-Stokes Equations : Theory & Numerical Methods (ed.by R.Salvi).. (to appear). (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Ikeda,H.Ikeda and M.Mimura: "Hopf bifurcation of travelling pulses in some bistable reaction-diffusion systems"Methods and Applications of Analysis. Vol.7. 165-194 (2000)

    • Related Report
      2000 Annual Research Report

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Published: 2000-04-01   Modified: 2016-04-21  

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