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1996 Fiscal Year Final Research Report Summary

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)
Project Period (FY) 1995 – 1996
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
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.

  • Research Products

    (31 results)

All Other

All Publications (31 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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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

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Published: 1999-03-09  

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