• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Co-operative Research on Numerical Solutions in Seience and Technology

Research Project

Project/Area Number 07304022
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section総合
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionHIROSHIMA UNIVERSITY

Principal Investigator

TABATA Masahisa  Hiroshima Univ., Faculty of Science, Professor, 理学部, 教授 (30093272)

Co-Investigator(Kenkyū-buntansha) YAMAMOTO Tetsurou  Ehime Univ., Dept. of Mathematics, Professor, 理学部, 教授 (80034560)
MITSUI Taketomo  Graduate School of Nagoya Univ., Dept. of Human Information, Professor, 大学院・人間情報学研究科, 教授 (50027380)
NAKAO Mitshuhiro  Graduate School of Kyushu Univ., Dept. of Mathematics, Professor, 大学院・数理学研究科, 教授 (10136418)
KAWARADA Hideo  Chiba Univ., Faculty of Engineering, Professor, 工学部, 教授 (90010793)
OKAMOTO Hisashi  Kyoto Univ, .Research Institute of Mathematical Science Professor, 数理解析研究所, 教授 (40143359)
友枝 謙二  大阪工業大学, 工学部, 教授 (60033916)
篠原 能材  徳島大学, 工学部, 教授 (40035803)
加古 孝  電気通信大学, 電気通信学部, 教授 (30012488)
Project Period (FY) 1995 – 1996
Project Status Completed (Fiscal Year 1996)
Budget Amount *help
¥7,400,000 (Direct Cost: ¥7,400,000)
Fiscal Year 1996: ¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 1995: ¥4,100,000 (Direct Cost: ¥4,100,000)
Keywordsfinite element method / drag and lift / vortex method and vortex sheet / leak boundary condition / domain decomposition method / parallel computation algorithm / Navier-Stokes equations / computation with guaranteed error bounds / 並列計算 / 自由境界問題 / 差分微分方程式 / 数値解の誤差評価 / 数値流体力学 / 反応拡散方程式系 / SOR-ニュートン法
Research Abstract

1. When the problem is axisymmetric, we can transform original three-dimensional problems to two-dimensional ones by introducing cylidrincal coordinates. The amount of required computation is reduced drastically but a singularity appears on the axis of symmetry. We have introduced suitable finite element subdivisions and weighted function spaces adapted to the singularity and obtained convergence results and optimal error estimates for both mixed and stabilized finite element approximations to flow problems.
2. We have developed a new method for getting much more precise force exerted from fluid to bodies in flows. Using a weak form we transform the surface integrals to body integrals for the computation of drag and lift forces. We have establish error analyzes and found more precise values of drag and lift coefficients of bodies of any shape.
3. The vortex layr is one of main fundamental processes of the turbulence and it is important ot find out the mechanism. We have studied numerically the behavior of two-dimensional vortex leyers in shear flows. We have observed that the phenomena differ much depending on the signs of vortices of vortex layrs and shear layrs.
4. Leak boundary conditions often appear in phenomena of engineering and environmental problems. We have formulated and analyzed the boundary condition. We have also developed a unmerical method.
5. We have combined higher-order finite elements and a residual iteration method in order to estimate errors of numerical solutions of nonlinear elliptic problems in the maximum norm. We have improved drastically the verification accuracy of numerical solutions.
6. We have proposed collocation type two-step Runge-Kutta methods. They preserve the orders and stability and are easily implemented on parallel computers. We have constructed higher-order two-step Runge-Kutta methods by a suitable setting of collocation points, implemented it in the prediction and correction type, and realized a high-performance computation.

Report

(3 results)
  • 1996 Annual Research Report   Final Research Report Summary
  • 1995 Annual Research Report
  • Research Products

    (52 results)

All Other

All Publications (52 results)

  • [Publications] M.Tabata: "Precise computation of drag coefficients of the sphee" The International Journal of Computational Fluid Dynamics. (印刷中). (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.Sakajo: "Numerical computation of vortex sheet roll-up in the background shear flow" Fluid Dynamics Research. 17. 195-212 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] H.Fujita: "Analytical and numerical approaches to stationary flow problems with leakand slip boundary conditions" Lecture Notes in Numerical and Applied Analysis. 14. 17-31 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M.T.Nakao: "Numerical verification of solutions for nonlinear elliptic problems using L^∞ residual method" Journal of Mathematical Analysis and Applications. (印刷中). (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] N.H.Cong: "Collocation-based two-step Runge-Kutta methods" Japan Journal of Industrial and Applied Mathematics. 13. 171-183 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 田端正久: "有限要素法による流れ問題の数値解析" 数学. 48. 22-36 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.Ikeda: "Numerical simulation for nonlinear oscillation of internal layers" Lecture Notes in Numerical and AppliedAnalysis. 14. 69-77 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] K.Ishihara: "On the optimum SOR iterations forfinite difference approximation to periodic boundary value problems." Mathematica Japonica. 41. 199-209 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] R.Fu: "Finite element analysis of free vibration of liquid-filled axisymmetric tanks" Acto Mathematicae Sppicatae Sinica. 12. 50-58 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] L.Deng: "Finite element approximation of eigenvalue problem for a coupled vibration between acoustic field and plate" Journal of Computational Mathematics,to appear.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] K.Tomoeda: "The possibility of a support splitting caused by the absorption in some nonlinear diffusion equations" New trends of inverse and ill-posed problems,VSP,the Netherlands,to appear.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.Nishida: "Bifurcation problems for the equations of fluid dynamics and computer aided proof." Lecture Notes in Numerical and Applied Analysis. 14. 145-157 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] S.Fujino: "ILU factorization well-suited to vector processor using a variant of 5-point difference scheme" Computer Physics Communications. 85. 371-381 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M.Mimura: "Pattern dynamics in an exothermic reaction" Physica D. 84. 58-71 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Kanayama,H.,Toshigami,K.,Tashiro,Y.,Tabata,M.,Fujima,S.: "Air flow computation around an automated guided vehicle" The International Journal of Computational Fluid Dynamics (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 藤井宏: "非線形力学" 岩波書店, 165 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 藤野清次: "反復法の数理" 朝倉書店, 140 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Mitsui,T.,Shinohara,Y.: "Numerical Analysis of Ordinary Differential Equations and its Applications" World Scientific Publications, 228 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M.Tabata and K.Itakura: "Precise computation of drag coefficients of the sphere." The International Journal of Computational Fluid Dynamics. (to appear.). (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.Sakajo and Okamoto: "Numerical computation of vortex sheet roll-up in the background shear flow." Fluid Dynamics Research. Vol.17. 195-212 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] H.Fujita, H.Kawarada and A.Sasamoto: "Analytical and numerical approaches to stationary flow problems with leak and slip boundary conditions." Lecture Notes in Numerical and Applied Analysis. Vol.14. 17-31 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M.T.Nakao and N.Yamamoyo: "Numerical verification of solutions for nonlinear elliptic problems using L^* residual method." Journal of Mathematical Analysis and Applications. (to appear.).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] N.H.Cong and T.Mitsui: "Collocation-based two-step Runge-Kutta methods" Japan Journal of Industrial and Applied Mathematics. Vol.13. 171-183 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.Ikeda: "Numerical simulation for nonlinear oscillation of internal layrs." Lecture Notes in Numerical and Applied Analysis. Vol.14. 69-77 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] K.Ishihara and M.Yamamoto: "On the optimum SOR iterations for finite difference approximation to periodic boundary value problems." Mathematica Japonica. Vol.41. 199-209 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] R.Fu and T.Ushijima: "Finite element analysis of free vibration of liquid-filled axisymmetric tanks." Acto Mathematicae Sppicatae Sinica. Vol.12. 50-58 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] L.Deng and T.Kako: "Finite element approximation of eigenvalue problem for a coupled vibration between acoustic field and plate" Journal of Computational Mathematics. (to appear.).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] K.Tomoeda and T.Nakaki: "The possibility of a support splitting caused by the absorption in some nonlinear diffusion equations." New trends of inverse and ill-posed problems, VSP,the Netherlands. (to appear.).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.Nishida, Y.Teramoto and H.Yoshihara: "Bifurcation problems for the equations of fluid dynamics and computer aided proof." Lecture Notes in Numerical and Applied Analysis. Vol.14. 145-157 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] S.Fujino and T.Takeuchi: "ILU factorization well-suited to vector processor using a variant of 5-point difference scheme." Computer Physics Communications. Vol.85. 371-381 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M.Mimura, N.Nagayama and K.Sakamoto: "Pattern dynamics in an exothermic reaction." Physica D. Vol.84. 58-71 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M. Tabata: "Precise computation of drag coefficients of the sphere" The International Journal of Computational Fluid Dynamics. (印刷中). (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] T. Sakajo: "Numerical computation of vortex sheet roll-up in the background shear flow" Fluid Dynamics Research. 17. 195-212 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] H. Fujita: "Analytical and numerical approaches to stationary flow problems with leak and slip boundary conditions" Lecture Notes in Numerical and Applied Analysis. 14. 17-31 (1995)

    • Related Report
      1996 Annual Research Report
  • [Publications] M. T. Nakao: "Numerical verification of solutions for nonlinear elliptic problems using L_∞ residual method" Journal of Mathematical Analysis and Applications. (印刷中). (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] N. H. Cong: "Collocation-based two-step Runge-Kutta methods" Japan Journal of Industrial and Applied Mathematics. 13. 171-183 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 田端正久: "有限要素法による流れ問題の数値解析" 数学. 48. 22-36 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 藤井宏: "岩波書店" 非線形力学, 165 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 藤野清次: "朝倉書店" 反復法の数理, 140 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 田端正久: "有限要素法による流れ問題の数値解析" 数学. 48. 22-36 (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] Kanayama, H.: "Air flow computation around an automated guided vehicle" The International Journal of Computational Fluid Dynamics. (to appear).

    • Related Report
      1995 Annual Research Report
  • [Publications] Ishihara, K.: "On the optimum SOR iterations for finite difference approximation to periodic boundary value problems" Mathematica Japonica. 41. 199-209 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Ishihara, K.: "Optimum SOR iterations for finite difference equations arising from nonlinear periodic boundary value problems" Mathematica Japonica. (to appear).

    • Related Report
      1995 Annual Research Report
  • [Publications] Li, D.: "Finite element approximation of eigenvalue problem for a coupled vibration between acoustic field and plate" Journal of Computational Mathematics. (to appear).

    • Related Report
      1995 Annual Research Report
  • [Publications] Cong, N. H.: "Collocation-based two-step Runge-Kutta methods" Japan Journal of Industrial and Applied Mathematics(to appear).

    • Related Report
      1995 Annual Research Report
  • [Publications] Saito, Y.: "Stability analysis of numerical schemes for stochastic differential equations" SIAM Journal on Numerical Analysis. (to appear).

    • Related Report
      1995 Annual Research Report
  • [Publications] 山本哲朗: "Durand-Kerner法に関する注意" 日本応用数理学会論文誌. 4. 251-258 (1994)

    • Related Report
      1995 Annual Research Report
  • [Publications] Kanno, S.: "On some methods of the simultaneous determination of polynomial zeros" Japan Journal of Industrial and Applied Mathematics. (to appear).

    • Related Report
      1995 Annual Research Report
  • [Publications] Yamamoto, N.: "Numerical verification for solutions to elliptic equations using residual iterations with higher order finite element" Jounal of Computational and Applied Mathematics. 60. 271-279 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Watanabe, Y.: "Verified computation of solutions for nondifferentiable elliptic equations related to MHD equilibria" Nonlinear Analysis. (to appear).

    • Related Report
      1995 Annual Research Report
  • [Publications] Ikeda,T.: "Numerical simulation for nonlinear oscillation of internal layers" Lecture Notes in Numerical and Applied Analysis. 14. 69-77 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Mitsui, T.: "Numerical Analysis of Ordinary Differential Equations and its Applications" World Scientific Publications, 228 (1995)

    • Related Report
      1995 Annual Research Report

URL: 

Published: 1995-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi