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Mathematical analysis of flows directly associated with environmental problems.

Research Project

Project/Area Number 10640100
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 InstitutionIbaraki University

Principal Investigator

ONISHI Kazuei  Ibaraki Univ., Faculty of Sci., Prof., 理学部, 教授 (20078554)

Co-Investigator(Kenkyū-buntansha) FUJIMA Shohiti  Ibaraki University., Faculty of Sci., Assoc. Prof., 理学部, 助教授 (00209082)
HASEGAWA Hiroshi  Ibaraki Univ., Faculty of Sci., Assoc. Prof., 理学部, 助教授 (70282283)
SAKATA Fumihiko  Ibaraki Univ., Faculty of Sci., Prof., 理学部, 教授 (50013438)
NAKAMURA Gen  Gunma Univ., Fac.Engng., Prof., 工学部, 教授 (50118535)
SHIROTA Kenji  Ibaraki University., Faculty of Sci., Assis. Prof., 理学部, 助手 (90302322)
日合 文雄  東北大学, 大学院・情報科学研究科, 教授 (30092571)
Project Period (FY) 1998 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 2000: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1999: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1998: ¥1,200,000 (Direct Cost: ¥1,200,000)
KeywordsWater environment / Atmospheric environment / Navier-Stokes equations / Shallow water equations / Finite element method / Finite analytical method / κ-εmodel / Dirichlet-Neumann alternating method / 環境流れ / 数値流体力学 / ナビエ・ストークスの方程式 / 乱流 / k-ε(ケイ・イプシロン)モデル / コンピュータ・シミュレーション
Research Abstract

The purpose of the research project is to investigate mathematical problems in the flow analysis closely connected with the problems of environmental pollution. The research aimes at the development of computer simulation techniques for the protection of the environment in the aquious and atmospheric fields. For the objectives, we obtain the following results :
1. The finite element method is used for numerical solution of flow equations in order to cope with the complex geometry of the flow domian in question. The governing equations are discretized by using the fractional step scheme for incompressible viscous fluid flow and using the Taylor-Galerkin's method for the flow in shallow waters.
2. Boundary conditions are discussed from the view points of the domain decomposition method and the inverse problems. When relatively small areas are considered for numerical simulation of environmental flow problems, artificial boundaries need to be introduced in the formulation, on which some for … More ms of fictitious boundary values should be prescribed. The values to be prescribed on the artificial boundaries play the crucial role for the success of the simulation. However the boundary values are not known a priori, in fact they constitute unknowns of the problem itself. We found from our numerical experiment on the flow simulation around airfoils that appropriate boundary values can be obtained by the Dirichlet-Neumann alternating method after quite a few times of iteration.
3. Laminar flow model turns out to be insufficient for the numerical simulation of flows in the environmental study. We extended our analysis to turbulent models. We concluded that the κ-ε model is the most suitable from the stand points of practical use ; (1) the model is easy-to-use, and (2) data requisite for the implementation of the model are easily accessible. For flows at high Reynolds numbers or order 10^5 in turbulent regime, the finite analytical method was applied for the numerical simulation. The simulation showed good agreement with the corresponding results in physical experiment. Less

Report

(4 results)
  • 2000 Annual Research Report   Final Research Report Summary
  • 1999 Annual Research Report
  • 1998 Annual Research Report
  • Research Products

    (45 results)

All Other

All Publications (45 results)

  • [Publications] K.Onishi and Y.Ohura: "Direct method of solution for general boundary value problem of the Laplace equation."Boundary Elements-WIT Press. XXII. 203-210 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] S.-W.Yan,F.Sakata,Y.-Z.Zhuo and X.-Z.Wu: "Dynamic realization of transport phenomenon in finite system."Physical Reviews. E63. 02116-1/14 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Hasegawa,T.Washio,Y.Ishimiya,and T.Saito: "Nonequilibrium thermodynamics from time series data analysis."Springer Lecture Notes of Artificial Intelligence. 1967. 304-305 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 藤間昌一: "A domain-decompasition finite-element scheme for flow problems -Choice of elements-"京都大学・数理解析研究所講究録. 1129. 9-22 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] K.Shirota,G.Nakamura,and K.Onishi: "Impedance computed tomo-electrocardiography"Chapman & Hall/CRC Research Notes in Mathematics. 419. 155-164 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] G.Nakamura and T.Tsuchida: "Uniqueness for an inverse boundary value problem for Dirac operator."Communications in Partial Differential Equations. 25. 1327-1369 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 登坂宣好,大西和榮,山本昌宏: "逆問題の数理と解法"東京大学出版会. 294 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 川原睦人,藤間昌一 他: "有限要素法による流れのシミュレーション"日本数値流体力学会有限要素法研究委員会(編),シュプリンガー・フェアラーク東京. 298 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] K.Onishi and Y.Ohura: "Direct method of solution for general boundary value problem of the Laplace equation."Boundary Elements-WIT Press. XXII. 203-210 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] S.-W.Yan, F.Sakata, Y.-Z.Zhuo, and X.-Z.Wu: "Dynamic realization of transport phenomenon in finite system"Physical Review. E63. 02116-1/14 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Hasegawa, T.Washio, Y.Ishimiya, and T.Saito: "Nonequilibrium thermodynamics from time series data analysis."Springer Lecture Notes of Artificial Intelligence.. 1967. 304-305 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] S.Fujima: "A domain-decomposition finite-element scheme for flow problems-Choice of elements-. Research Institute of Mathematical Sciences"Kyoto University. Vol.1129. 9-22 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] K.Shirota, G.Nakamura, and K.Onishi: "Impedance computed tomo-electrocardiography"Chapman & Hall/CRC Research Notes in Mathematics. Vol.419. 155-164 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] G.Nakamura and T.Tsuchida: "Uniqueness for an inverse boundary value problem for Dirac operator."Communicationa in Partial Differential Equations. Vol.25. 1327-1369 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] N.Tosaka, K.Onishi, and M.Yamamoto: "Mathematics and Solutions of Inverse Problems."Tokyo University Publications. 1-294 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Kawahara, S.Fujima, et al.: "Flow Simulation Using Finite Element Methods."Springer-Verlag Tokyo. 1-298 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Q.Wang and K.Onishi: "Numerical reconstruction of internal states by boundary measurements for the Laplace equation."Numerical Functional Analysis and Optimization. 印刷中(発表予定).

    • Related Report
      2000 Annual Research Report
  • [Publications] S.W.Yan,F.Sakata,Y.Z.Zhuo,and X.Z.Wu: "Dynamic realization of transport phenomenon in finite system."Physical Reviews. E63. 021116 1-14 (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] 藤間昌一: "A domain-decomposition Cinite-element scheme for flow problems-Choice of elements-"数理解析研究所講究録・京都大学. 1129. 9-22 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] K.Shirota,K.Onishi,and G.Nakamura: "Inverse boundary value problem with the unknown material."Theoretical and Applied Mechanics. 47. 315-323 (1998)

    • Related Report
      2000 Annual Research Report
  • [Publications] G.Nakamura,S.Saitoh,and A.Syarif: "Representation and harmonic extension formulas of harmonic functions on half spaces"Complex Variables Theory and Applications. 42. 323-332 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Aoki and M.Yamamoto: "Development of 3-dimensional blade design system using virtual reality technique."Journal of Flow Visualization and Image Processing. 17・1. 51-62 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] F.Sakata: "Frontiers of Theoretical Physics"World Scientific. 296 (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] G.Nakamura,S.Saitoh,J-K.Seo,and M.Yamamoto: "Inverse Problem. and Related Topics"Chapman & Hall / CRC. 233 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Y.Ohura,K.Kobayashi,and K.Onishi: "Numerical solution of an under-determined problem of the Laplace equation."Journal of Applied Mechanics,JSCE. 2. 185-189 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] H.Hasegawa,T.Washio,and Y.Ishimiya: "Thermodynamics from time series data analysis."Lecture Notes in Artificial Intelligence. 1721. 326-327 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] S.Fujima: "Mortar element method for flow problems in primitive variables form."International Journal of Computational Fluid Dynamics. 9. 209-219 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] T.Shigeta,T.Harayama,and K.Shirota: "Combination of the finite and the boundary element methods for an external boundary value problem of the Poisson equation."Journal of the Chinese Institute of Engineers. 22・6. 777-782 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] G.Nakamura and G.Uhlmann: "Inverse scattering at a fixed energy for elasticity."Journal of Inverse and Ill-posed Problems. 7. 283-288 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] K.Ona and M.Yamamoto: "Numerical investigation of spiral water jet."Proceedings of Joint ASME/JSME Fluids Engineering. ASME FEDSM 99・7258. 1-6 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 登坂宣好,大西和栄,山本昌宏: "逆問題の数理と解法"東京大学出版会. 294 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 川原睦人,奥田洋司,藤間昌一,他: "有限要素法による流れのシミュレーション"シュプリンザー・フェアラーク東京. 298 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] K.Shirota,K.Onishi,et al.: "Inverse boundary value problem with unknown material." Theoretical and Applied Mechanics. 47. 315-323 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Kobayashi,K.Onishi,et al.: "An approximate variational method for the Cauchy problem in plane elastostatics." Theoretical and Applied Mechanics. 47. 341-347 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Hasegawa et al.: "Mechanisms of self-organized renormalizability" Lecture Notes in Artificial Intelligence. 1532. 391-392 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 長谷川 博, 他: "雑音下の繰り込み可能性の安定性について" 情報処理学会全国大会論文集. 98. 87-90 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] F.Hiai: "Maximizing free entropy." Acta Math.Hungar.80・4. 335-356 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] F.Hiai: "Amenability and strong amenability for fusion algebras with applications to subfactor theory." Internat.J.Math.9・6. 669-722 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Kawashita,G.Nakamura: "The poles of the resolvent for the exterior Neumann problem of anisotropic elasticity." SIAM J.Math.Anal.発表予定.

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Ikehata,G.Nakamura et al.: "Identification of the shape of inclusion of anisotropic elastic body." Applicable Analysis. 発表予定.

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Danbara,M.Yamamoto et al.: "Modeling of boundary condition for turbulent boundary layer bleed." AIAA Paper. 98・926. 1-9 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Toda,M.Yamamoto,et al.: "Computation of supersonic turbulent flowfield with secondary jet normal to freestream." AIAA Paper. 98・944. 1-9 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Fujima: "Iso-P2 P1/P1/P1 domain-decomposition/finite-element method for the Navier-Stokes equations." Contemporary Mathematics. 218. 246-253 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Fujima: "Mortar element method for flow problems in primitive variables form." Internat.J.Computatinal Fluid Dynamics. 9. 209-219 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 川原睦人,藤間昌一,他: "有限要素法による流れのシミュレーション" シュプリンガー・フェアラーク東京, 298 (1998)

    • Related Report
      1998 Annual Research Report

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Published: 1998-04-01   Modified: 2016-04-21  

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