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Development of New Numerical Methods Based on Locally Exact Differencing and Numerical Investigation on Naturally Convected Heat Transfer

Research Project

Project/Area Number 05680420
Research Category

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

Allocation TypeSingle-year Grants
Research Field エネルギー学一般・原子力学
Research InstitutionSaitama Institute of Technology

Principal Investigator

SAKAI Katsuhiro  Saitama Institute fo Technology, Faculty of Eng. Asso. Prof., 工学部, 助教授 (60153839)

Project Period (FY) 1993 – 1995
Project Status Completed (Fiscal Year 1995)
Budget Amount *help
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1995: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1994: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1993: ¥500,000 (Direct Cost: ¥500,000)
Keywordsfinite difference method / numerical analysis / transport equation / high-order numerical scheme / numerical oscillations / natural convection / cavity flow / naturally convected heat transfer
Research Abstract

1) A new umerical scheme LENS for the convection term was developed on a base of locally exact numerical differencing, in which difference coefficients are determined such that the resulting diffcrence equation satisfies the exact solution of transport equations with the absorption and source terms at nodal points.
2) The LENS scheme was improved so that the spatial distribution of the coefficients in the transport equations is taken into consideration based on a two-region model in a control volume.
3) Numerical stability analysis showed that solutions with the LENS scheme are free from numerical oscillations for any value of transporting velocities and absorption.
4) The mass, momentum and energy equations were discretized using the LENS scheme and a 2-D thermal hydraulics analysis program was developed.
5) The above computer program was validated through numerical experiments for the plane Poiseuille flow and the Karman vortex shedding.
6) The numerical simulation using the present computer program was performed for naturally circulating flows with high Rayleigh numbers Ra=10^8-10^<10> in a square cavity, where conventional numerical methods tend to suffer from large numerical diffusions and unstable solutions because of strong thermohydraulics coupling in multidimensional fields. Steady solutions were obtained in case of Ra=10^8 However, in case of Ra=10^<10> the solutions were not steady but temporally dependent. Developing of vortex formation and the chaotic structure of vortex after the temperature difference was imposed on the walls were made numerically investigated.

Report

(4 results)
  • 1995 Annual Research Report   Final Research Report Summary
  • 1994 Annual Research Report
  • 1993 Annual Research Report
  • Research Products

    (60 results)

All Other

All Publications (60 results)

  • [Publications] Katsuhiro Sakai: "Development of Locally Exact Numerical Scheme (LENS) for Transport Equation with Source Terms" Compu. Fluid Dynamics JOURNAL. 2. 161-168 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Katsuhiro Sakai: "Optimized Locally Exact Numerical Scheme Based and on Finite Variable Difference Method Characteristic Polynomial Analysis Method" J. Nuci. Sci. Technol.32. 42-49 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Katsuhiro Sakai: "New Numerical Schemes Based on a Criterion for Constructing Essentially Stable and Accurate Numerical Schemes for Convection-Dominated Equations" Int. J. Numer. Methods in Fluids. 21. 1041-1048 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Katsuhiro Sakai: "A New Numerical Scheme for Convection-Dominated Transport Equations" A New Numerical Scheme for Convection-Dominated Transport Equations. 32. 34-42 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Katsuhiro Sakai: "A New Finite Variable Difference Method with Application to Locally Exact Numerical Scheme LENS" J. Comput. Physics. 124. (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Katsuhiro Sakai: "An Extended Finite Variable Difference Method with Application to QUICK scheme-Optimized QUICK" J. Nucl. Sci. Technol.33. (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Katsuhiro Sakai: "A Locally Exact Numerical Scheme with Nonoscillations Properties for Transport Equations with Absorption and Source Terms" Nucl. Sci. Eng.122. (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Katsuhiro Sakai: "New Numerical Schemes Essentially Stable and Accurate for Convection-Dominated Transport Equations" 第8回数値流体力学シンポジューム講演論文集. 499-502 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Katsuhiro Sakai: "A New Finite Variable Difference Method and its Application for LENS and QUICK Schemes Using CharacteristicPolynomial Analysis Method" 第8回数値流体力学シンポジューム講演論文集. 503-506 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Katsuhiro Sakai: "Nonlocally Exact Numerical Scheme" 第9回数値流体力学シンポジューム講演論文集. 111-112 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 酒井勝弘: "有限可変差分法と特性多項式解析法に基づき最適化された局所解析法スキームソース項のない対流・拡散方程式の場合" 第5回計算流体力学シンポジューム講演要旨集. 9-9 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 酒井勝弘: "有限可変差分法の拡散とQUICKスキームへの適用-OQUICKスキーム" 第6回計算流体力学シンポジューム講演要旨集. 7-7 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 酒井勝弘: "有限可変差分法と特性根の極値性に基づく新差分法" 第45回応用力学連合講演会講演予稿集. 65-66 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 酒井勝弘、佐藤泰助、乙部新一: "Development of Locally Exact Numerical Scheme for Transport Equations with Source Terms" 第48回情報処理学会全国大会講演論文集(1). 133-134 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Katsuhiro Sakai: "Developmet of Locally Exact Numerical Scheme LENS Essentially Stable for All Mesh Reynolds Number(1)-Spatially Dependent Coefficients" J. Saitama Institute of Tecnology. 3. 45-53 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Katsuhiro Sakai: "A New Finite Variable Difference Method and Its Application to Locally Exact Numerical Scheme LENS using Characteristic Polynomial Analysis Method"" J. Saitama Institute of Tecnology. 4. 39-52 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Katsuhiro Sakai: "An Adjusted QUICK Scheme Based on A New Finite Variable Difference Method and Characteristic Polynomial Analysis Method" J. Saitama Institute of Tecnology. 4. 53-66 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 酒井勝弘、張根生: "局所解析解高次精度差分法LENSスキームの数値的安定性解析" 埼玉工業大学紀要. 5. 117-122 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Katsuhiro Sakai: "A Locally Exact Numerical Scheme LENS Essentially Stable for Transport equation with Source Terms" Proceeding of the 7th Int. Conference on Boundary and Interior Layers Computational and Asymptotic Methods at Beijing, China. 117-122 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Katsuhiro Sakai: "An Optimized Locally Exact Numerical Scheme based on a Finite Variable Difference Method" Proccding of the First Asian Computational Fluid Dynamics Conferencc at Hong Kong. 931-936 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Katsuhiro Sakai: "A New Finite Variable Difference Method with Application to Nolinear Burgers Equation" Second World Congress of Nolinear Analysis at Athens, Greece. 10-17 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 酒井勝弘: "特性根が極を持つというクライテリアに基づいた新差分スキーム" 日本原子力学春の年会要旨集. 44 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Sakai: "Development of Locally Exact Numerical Scheme (LENS) for Transport Equation with Source Terms" Compu.Fluid Dynamics JOURNAL. 2. 161-168 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Sakai: "Optimized Locally Exact Numerical Scheme Based On Finite Variable Difference Method and Characteristic Polynomial Analysis Method" J.Nucl.Sci.Technol.32. 42-49 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Sakai: "New Numerical Schemes Based on a Criterion for Constructing Essentially Stable and Accurate Numerical Schemes for Convection-Dominated Equations" Int.J.Numer.Methods in Fluids. 21. 1041-1048 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Sakai: "A New Numerical Scheme for Convection-Dominated Transport Equations" J.Nucl.Sci.Technol. 32. 34-42 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Sakai: "A New Finite Variable Difference Method with Application to Locally Exact Numerical Scheme LENS" J.Comput.Physics. 124(in press). (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Sakai: "An Extended Finite Variable Difference Method with Application to QUICK scheme-Optimized QUICK" J.Nucl.Sci.Technol.33(in press). (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Sakai: "A Locally Exact Numerical Scheme with Nonoscillations Properties for Transport Equations with Absorption and Source Terms" Nucl.Sci.Eng.122(in press). (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Sakai: "Development of Locally Exact Numerical Scheme LENS Essentially Stable for All Mesh Reynolds Number(1)-Spatially Dependent Coefficients" J.Saitama Institute of Tecnology. 3. 45-53 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Sakai: "A New Finite Variable Difference Method and Its Application to Locally Exact Numerical Scheme LENS using Characteristic Polynomial Analysis Method" J.Saitama Institute of Tecnology. 4. 39-52 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Sakai: "An Adjusted QUICK Scheme Based on A New Finite Variable Differnce Method and Characteristic Polynomial Analysis Method" J.Saitama Institute of Tecnology. 4. 53-66 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Sakai: "Numerical Stability Analysis of Locally Exact Numerical Scheme LENS" J.Satitama Institute of Tecnology. 5. 51-57 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Sakai: "A Locally Exact Numerical Scheme LENS Essentially Stable for Transport equations with Source Terms" Proceeding of the 7th Int.Con.on Boundary and Interior Layrs Compu.and Asymptotic Methods at Beijing, China. 117-122 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Sakai: "An Optimized Locally Exact Numerical Scheme Based on a Finite Variable Difference Method" Proceeding of the 1st Asian Compu.Fluid Dynamics Conference at Hong Kong 7C-4. 931-936 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Sakai: "A New Finite Variable Difference Method with Application to Nolinear Burgers Equation" Second World Congress of Nolinear Analysis at Athens, Greece July 10-17. (to be presented). (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Sakai: "New Numerical Schemes Essentially Stable and Accurate for Convection-Dominated Transport Equations" The 8th CFD Sympojyum. C22-1. 499-502 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Sakai: "A New Finite Variable Difference Method and its Application for LENS and QUICK Schemes Using Characteristic Polynomial Analysis Method" The 8th CFD Sympojyum. C22-2. 503-506 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Sakai: "Nonlocally Exact Numerical Scheme" The 9th CFD Sympojyum. A9-1. 111-112 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Sakai: "An Optimized Locally Exact Numerical Scheme Based on A Finite Variable Difference Method and Characteristic Polynomial Method" The 5th CHD Sympojyum. C-3. 9-9 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Sakai: "Extension of Finite Variable Difference Method with Application to UICK Scheme" The 6th CHD Sympojyum. C-1. 7-7 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Sakai: "New Numerical Schemes Based on A Finite Variable Difference Method and a Criterion That Characteristic Roots have poles" The 45th Nat.Cong.of Theor. & Appl.Mech. 65-66 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Sakai: "Development of Locally Exact Numerical Scheme for Transport Equation with Source Terms" Proc.of Information Processing Society of Japan. 133-134 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Sakai: "New Numerical Schemes Based on a Criterion That Characteristic Roots Have Poles" Annual Meeting of the Atomic Energy Society of Japan. 44-44 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 酒井勝弘: "Development of Locally Exact Numerical Scheme (LENS) for Transport Equation with Source Terms" Computational Fluid Dynamics JOURNAL. 2. 161-168 (1993)

    • Related Report
      1994 Annual Research Report
  • [Publications] 酒井勝弘: "Locally Exact Numerical Scheme for Transport Equations with Source Terms" Trans.of American Nuclear Society. 68(A). 227-228 (1993)

    • Related Report
      1994 Annual Research Report
  • [Publications] 酒井勝弘: "Development of Locally Exact Numerical Scheme for Transport Equations with Source Terms" 情報処理学会講演論文集(1)第48回. 133-134 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] 酒井勝弘: "Development of Locally Exact Numerical Scheme LENS Essentially Stable for Any Mesh Reynolds number (I)" 埼玉工業大学紀要. 3. 45-53 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] 酒井勝弘: "有限可変差分法と特性多項式解析法に基づき最適化された局所解析解法スキーム-ソース項のない対流・拡散方程式の場合" 第5回計算流体力学シンポジュームC-3. 9-9 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] 酒井勝弘: "New Numerical Schemes Essentially Stable and Accurate for Transport-Dominated Equations" 第8回数値流体力学シンポジュームC22-1. 499-502 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] 酒井勝弘: "A New Finite Variable Difference Method and its Application for LENS and QUICK Schemes Using Characteristic Polynomial Analysis Method" 第8回数値流体力学シンポジュームC22-2. 503-506 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] 酒井勝弘: "Optimized Locally Exact Numerical Scheme Based on Finite Variable Difference Method and Characteristic Polynomial Analysis Method" J.Nuclear Science and Technology. 32. 42-49 (1995)

    • Related Report
      1994 Annual Research Report
  • [Publications] 酒井勝弘: "New Numerical Schemes Based on a Criterion in Constructing Schemes Stable and Accurate that Characteristic Roots have Poles" Int.J.Numerical Method in Fluids. (印刷中).

    • Related Report
      1994 Annual Research Report
  • [Publications] 酒井勝弘: "A New Finite Variable Difference Method I - Optimized Locally Exact Numerical Schemes" 埼玉工業大学紀要. 4(印刷中). (1995)

    • Related Report
      1994 Annual Research Report
  • [Publications] 酒井勝弘: "A New Finite Variable Difference Method II - Optimized Tayer Expansion Scheme QUICK" 埼玉工業大学紀要. 4(印刷中). (1995)

    • Related Report
      1994 Annual Research Report
  • [Publications] 酒井勝弘: "特性根が極をもつというクライテリヤに基づく新差分スキーム" 1995年日本原子力学会年会A44. (発表予定). (1995)

    • Related Report
      1994 Annual Research Report
  • [Publications] 酒井勝弘: "Development of Locally Exact Numerical Scheme(LENS)for Transport Equation with Source Terms" Computational Fluid Dynamics JOURNAL. 2. 161-168 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] 酒井勝弘: "Locally Exact Numerical Scheme for Transport Equations with Source Terms" Trans.Amer.Nucl.Soc.69. 227-228 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] 酒井勝弘: "Development of Locally Exact Numerical Scheme for Transport Equations with Source Terms" 情報処理学会講演論文集(1). 第48回(1). 133-134 (1994)

    • Related Report
      1993 Annual Research Report
  • [Publications] 酒井勝弘: "Development of Locally Exact Numerical Scheme LENS Essentially Stable for Any Mesh Reynolds number(I)" 埼玉工業大学紀要. 3(予定). (1994)

    • Related Report
      1993 Annual Research Report

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Published: 1993-04-01   Modified: 2016-04-21  

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