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Finite-Difference Schemes for 3-D Incompressible Viscous Flows in Curvilinear Coordinate Systems

Research Project

Project/Area Number 01550131
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field Fluid engineering
Research InstitutionTohoku University

Principal Investigator

IKOHAGI Toshiaki  Tohoku Univ., Dept. Mech. Eng., Asso. prof., 工学部, 助教授 (90091652)

Co-Investigator(Kenkyū-buntansha) DAIGUJI Hisaaki  Tohoku Univ., Dept. Mech. Eng., Prof., 工学部, 教授 (70005239)
Project Period (FY) 1989 – 1990
Project Status Completed (Fiscal Year 1990)
Budget Amount *help
¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 1990: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1989: ¥1,000,000 (Direct Cost: ¥1,000,000)
KeywordsComputational Fluid Dynamics / Incompressible Viscous Flow / Navier-Stokes Equation / Finite-Difference Method / General Curvilinear Coordinate Systems / Contravariant Velocity / Upstream-difference / High Reynolds Number Flow
Research Abstract

In order to analyze numerically the 3-D incompressible viscous flows with complex geometries, efficient finite-difference schemes and their computing programs have been developed.
Since the present scheme deals with the contravariant velocity as unknown variable in contrast with the conventional approach, in which the physical velocities are computed in a transformed space, it is possible to treat accurately the solid and cyclic boundary conditions, and to introduce easily a turbulence model into the scheme. First, the momentum equations of contravariant velocity components in curvilinear coordinate systems were newly derived from the Navier-Stokes equations. Second, an explicit time-marching finite-difference scheme extended to the curvilinear coordinate grid by using SMAC method or the fractional step method, was proposed. Employing a staggered grid in the transformed space in a similar manner to MAC method, the continuity condition can be satisfied identically and the occurrence of s … More purious error in pressure can be removed completely. Third, applying the trapezoidal rule, an implicit scheme was developed, in which the approximate factorization method and the partial consideration of viscous terms for the implicit portion are taken in order to enhance the stability of the scheme and to save the computational time. In the both explicit and implicit schemes, the momentum equations of contravariant velocities have been solved by discretising the convective term with QUICK scheme or thirdorder TVD scheme. Numerical simulations of stepped duct flows, cavity flow and rotor flow of axial-flow blower have shown the validity of the present schemes. Furthermore, the above-mentioned implicit scheme was also extended to an unsteady flow scheme by applying the Crank-Nicholson scheme and Newton iteration method. Direct numerical simulations were performed for the high Reynolds number flows in 2-D stepped duct and through a cascade. The evolution of shedding vortices into the wake from trailing-edge and the vortex behavior in the recirculating zone behind a step were able to be visualized. Less

Report

(3 results)
  • 1990 Annual Research Report   Final Research Report Summary
  • 1989 Annual Research Report
  • Research Products

    (20 results)

All Other

All Publications (20 results)

  • [Publications] T.Ikohagi: "FiniteーDifference Schemes for Steady Incompressible NavierーStokes Equations in General Curvilinear Coordinates" A Collection of Technical Papers of 3rd Int.Symp.on Comp.Fluid Dyn.ー Nagoya. 653-658 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] T.Ikohagi: "An Implicit FiniteーDifference Scheme for the Steady 3ーD Incompressible NavierーStokes Equations in Curvilinear Coordinates and its Application" Proc.3rd JapanーChina Joint Conf.Fluid Machinery ー Osaka. II. 227-234 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 申 炳録: "定常非圧縮性ナビエ・スト-クス方程式の曲線座標格子に適用できる効率的差分スキ-ム" 日本機械学会論文集 B編. 56ー525. 1357-1363 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] T.Ikohagi: "Application of an Implicit Timeーmarching Scheme to 3ーD Incompressible Flow Problem in Curvilinear Coordinate Systems" Proc.2nd JapanーSoviet Union Symp.Comput.Fluid Dyn.ー Tsukuba.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] B.R.Shin: "Numerical Simulation of the Unteady Wake in 2ーD Incompressible Cascade Flows" Proc.2nd KSMEーJSME Fluid Engng.Conf.ー Seoul. 1. 440-445 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] T.Ikohagi: "An Implicit SMAC Scheme Using Curvilinear Coordinate Grid" Rep.Institute of Fluid Science,Tohoku Univ.1. 87-102 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Ikohagi, T. and Shin, B. R.: "Finite-Difference Schemes for Steady Incompressible Navier-Stokes Equations in General Curvilinear Coordinates" A Collection of Technical Papers of 3rd Int. Symp. on Comp. Fluid Dyn. -Nagoya. 653-658 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Ikohagi, T., Shin, B. R. and Daiguju, H.: "An Implicit Finite-Difference Scheme for the Steady 3-D Incompressible Navier-Stokes Equations in Curvilinear Coordinates and Its Application" Proc. 3rd Japan-China Joint Conf. Fluid Machinery-Osaka. Vol. II. 227-234 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Shin, B. R., Ikohagi, T. and Daiguji, H.: "An Efficient Finite-Difference Scheme for the Steady Incompressible Navier-Stokes Equations Using a Curvilinear Coordinate Grid" Trans. JSME. Vol. 56-525, Series B. 1357-1363 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Ikohagi, T., Shin, B. R. and Daiguji, H.: "Application of an Implicit Time-marching Scheme to 3-D Incompressible Flow Problem in Curvilinear Coordinate Systems" Proc. 2nd Japan-Soviet Union Symp. Comput. Fluid Dyn. -Tsukuba. (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Shin, B. R., Ikohagi, T. and Daiguji, H.: "Numerical Simulation of the Unsteady Wake in 2-D Incompressible Cascade Flows" Proc. 2nd KSME-JSME Fluid Engng. Conf. -Seoul. Vol. 1. 440-445 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Ikohagi, T., Shin, B. R. and Daiguji, H.: "An Implicit SMAC Scheme Using Curvilinear Coordinate Grid" Rep. Institute of Fluid Science, Tohoku Univ.Vol. 1. 87-102 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Ikohagi,T: "An Implicit FiniteーDifference Scheme for the Steady 3ーD Incompressible NavierーStokes Equetions in Curvilinear Coordinates and Its Application" Proc.3rd JapanーChina Joint Conf.Fluid MachineryーOsaka. II. 227-234 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] Ikohagi,T: "Application of an Implicit Timeーmarching Scheme to 3ーD Incompressible Flow Problem in Curvilinear Coordinate Systems" Proc.2nd JapanーSoviet Union Symp.Comput.Fluid Dyn.ーTsukuba(also Computers & Fluids). (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] Shin,B.R.: "Numerical Simulation of the Unsteady Wake in 2ーD Incompressible Cascade Flows" Proc.2nd KSMEーJSME Fluid Engng.Conf.ーSeoul. 1. 440-445 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] Ikohagi,T: "On Algebraic Expression for the Reynolds Stresses" Proc.First Joint ASMEーJSME Fluids Engng.Conf.(1991)

    • Related Report
      1990 Annual Research Report
  • [Publications] T.Ikohagi: "Finite-Difference Schemes for Incompressible Navier-Stokes Equations in General Curvilinear Coordinates" Preprints of Int.Symp.on Computational Fluid Dynamics--Nagoya. 653-658 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] 井小萩利明: "二次元非圧縮翼列流れの非定常ナビエ・スト-クス解析" 第3回数値流体力学シンポジウム講演論文集. 475-478 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] T.Ikohagi: "An Implicit Finite-Difference Scheme for the Steady 3-D Incompressible Navier-Stokes Equations in Curvilinear Coordinates and Its Applications" The 3rd Japan-China Joint Conference on Fluid Machinery. (1990)

    • Related Report
      1989 Annual Research Report
  • [Publications] 申炳録: "定常非圧縮性ナビエ・スト-クス方程式の曲線座標格子に適用できる効率的差分スキ-ム" 日本機械学会論文集. (1990)

    • Related Report
      1989 Annual Research Report

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Published: 1989-04-01   Modified: 2016-04-21  

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