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

Development of Numerical Method for Mesoscopic Flow

Research Project

Project/Area Number 09680474
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field エネルギー学一般・原子力学
Research InstitutionTOKYO INSTITUTE OF TECHNOLOGY

Principal Investigator

YABE Takashi  Tokyo Institute of Technology interdisciplinary Graduate School of Science & Engineering, Professor, 大学院・総合理工学研究科, 教授 (60016665)

Co-Investigator(Kenkyū-buntansha) AOKI Takayuki  Tokyo Institute of Technology Nuclear Reactor Laboratory, Associate Professor, 原子炉工学研究所, 助教授 (00184036)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 1998: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1997: ¥2,400,000 (Direct Cost: ¥2,400,000)
KeywordsMesoscale / Numerical Method / CIP Method / Boltzmann / Vlasov / Particle Methods / Six Dimensions / Landau Damping / メソスケール / ボルツマン / ブラソク / 数値解法 / CIP / Euler法 / 粒子法 / スプライン法 / 数値解析 / CIP法 / ブラソフ / 6次元 / ランダウ減衰
Research Abstract

For the research of microscopic phenomena, molecular dynamics model has been proposed and for macroscopic level various kinds of hydrodynamic solvers have been investigated for a long time. In this research, we search for a numerical method to treat mesoscopic level that means the intermediate scale between and microscopic and macroscopic levels . For this purpose, we have used the CIP method which has been proposed by the author and has been proved to be accurate even with coarse grid system. In this research, we have used the Boltzmann equation which is six dimensions in phase space. Thus time evolution is merely an advection through six dimensions. Since the CIP method has been proved to be quite effective in solving advection equation, we applied this method and for simplicity we repeated one-dimensional CIP method to extend it to hyper-dimensional space.
In order to test the algorithm, we solved two and four dimensional Vlasov equation which is collisionless Boltzmann equation, and applied it to linear Landau damping and nonlinear two-stream instability coupled with electric fields.
Comparison with conventional particle codes and spline method has been done and it has been proven that particle codes need 10-100 times more memory than the CIP method for obtaining the same results. For a sufficiently accurate form of velocity distribution function required by mesoscopic calculations, particle codes needed 100 times more memory than the CIP method. Distribution functions given by spline methods become negative and have large spikes. These comparisons show the effectiveness of the CIP method in this research.
We have varied the velocity grids and found that even with velocity grids less than 10 the CIP can give quite an accurate result. Finally, six dimensional code has been constructed and run on personal computer. One Alpha-chip-based personal computer needed only 6.7 hours for the calculation of Landau damping with 16 X 16 X 16 X 8 X 8 X 8 grids.

Report

(3 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • Research Products

    (19 results)

All Other

All Publications (19 results)

  • [Publications] Feng XIAO, Takashi YABE, Tomoyoshi ITO and Masakazu TAJIMA: "An Algorithm for Simulating Solid Objects Suspended in Stratified Flow" Comput.Phys.Commun.102. 147-160 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hidekazu MAKUUCHI, Takayuki AOKI and Takashi YABE: "Implicit CIP(Cubic-Interpolated Propagation)Method in Two Dimensions" JSME International Journal. 40. 365-376 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] F.Xiao, T.Yabe and T.Ebisuzaki: "An Oscillation Suppressing Semi-Lagrangian Solver for Advection Equation" Comput.Phys.Commun.116. 121-135 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Y.Ogata and T.Yabe: "Shock Capturing with Improved Numerical Viscosity in Primitive Euler Representation" Comput.Phys.Commun.in press. (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Yoon and T.Yabe: "The Unified Simulation for Incompressible and Compressible Flow by Predictor-Corrector Scheme Based on CIP Method" Comput.Phys.Commun.in press. (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Nakamura and T.Yabe: "Cubic Interpolated Propagation Scheme for solving the Hyper-Dimensional Vlasov-Poisson Equation in Phase Space" Comput.Phys.Commun.in press. (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] R.Tanaka, T.Yabe and H.Wu: "A Class of Conservative Formulation of the CIP Method" CFD Journal. in press. (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Yabe: "Unified Solver for Solid, Liquid and Gas" CFD Review'98, (World Scientific), 17 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 田島雅和,渡辺和義,矢部孝: "CIP法による小型船体のスラミング現象のシミュレーション" 日本機械学会論文集(B編). 64巻618号. 63-70 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 矢部 孝: "固体・液体・気体の汎用シミュレーシュン手法(解説)" シミュレーション. 17巻・3号. 7-13 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 矢部 孝: "パルスレーザー加工・溶接現象のシミュレーション(解説)" レーザー研究. 26巻11号. 788-792 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Y.Ogata,T.Yabe: "Shock Capturing with Improved Numerical Viscosity In Primitive Euler Representation" Comput.Phys.Commun.(印刷中).

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Yoon,T.Yabe: "The Unified Simulation for Incompressible and Compressible Flow by Predicter-Corrector Scheme based on CIP Method" Conput.Phys.Commun.(印刷中).

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Yabe,Y.Zhang,F.Xiao: "A Numerical Procedure-CIP-to Solve All Phases of Matter Together" Proc.16th Int.Conf.Num.Meth.Fluid Dynamics. 439-457 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Yabe: "Mathematical Modeling of Weld Phenomena (分担)" The University Press,Cambridge, 683 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Yabe: "Computational Fluid Dynamics Review 1998 (分担)" World Scientific, 1130 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Makuuchi, T.Aoki, T.Yabe: "Implicit CIP Method in Two Dimensions" JSME Int. Journal. 40・3. 365-376 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 矢部孝: "CIP-計算力学の超解析法ー" 機械の研究. 49・1. 83-88 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 中村恭志,矢部孝: "CIP法によるVlasov,Boltzmann方程式の数値解法" 第11回数値流体シンポジウム講演論文集. 413-414 (1997)

    • Related Report
      1997 Annual Research Report

URL: 

Published: 1997-04-01   Modified: 2020-08-11  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi