TU Guo-hua, DENG Xiao-gang. Spectral property comparison of fifthorder nonlinear WCNS and WENO difference schemes[J]. ACTA AERODYNAMICA SINICA, 2012, 30(6): 709-712.
Citation: TU Guo-hua, DENG Xiao-gang. Spectral property comparison of fifthorder nonlinear WCNS and WENO difference schemes[J]. ACTA AERODYNAMICA SINICA, 2012, 30(6): 709-712.
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Spectral property comparison of fifthorder nonlinear WCNS and WENO difference schemes

  • 1.

    State Key Laboratory of Aerodynamics,China Aerodynamics Research and Development Center,Mianyang 621000,China

  • 2.

    Science and Technology on Scramjet Laboratory,Hypervelocity Aerodynamics Institute of CARDC,Mianyang 621000,China

  • 3.

    National University of Defense Technology,Changsha 410073,China

  • 4.

    Computational Aerodynamics Institute,China Aerodynamics Research and Development Center,Mianyang 621000,China

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  • Received Date: February 13, 2011
  • Revised Date: October 17, 2011
  • Available Online: January 07, 2021
    Graphical Abstract
    • Abstract
  • Approximate dispersion relation (ADR) may represent modified wave numbers of nonlinear schemes, and a numerical procedure is proposed to compute the ADR. The ADRs of the fifthorder nonlinear WENO5 and WCNS-E-5 finite difference schemes are compared with each other to show their spectral property. The results indicate that the dispersion error of the WCNS-E-5 is smaller than that of the WENO5, and the dissipation error of the WCNS-E-5 is also smaller than that of the WENO5. The whole spectral property of the WCNS-E-5 is better than that of the WENO5.
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    • References (13)
  • [1]
    张涵信,李沁,庄逢甘. 关于高阶差分格式的问题[J]. 空气动力学学报, 1998, 16(1): 14-23.
    [2]
    VICHNEVETSKY R, BOWLES J B. Fourier analysis of numerical approximations of hyperbolic equations[M]. Philadelphia: Society for Industry and Applied Mathematics, 1982.
    [3]
    LELE S K. Compact finitedifference schemes with spectral like resolution[J]. Journal of Computational Physics, 1992, 103: 16-42.
    [4]
    TAM C K W, WEBB J C. Dispersionrelationpreserving finite difference schemes for computational acoustics[J]. Journal of Computational Physics , 1993, 107(2): 262-281.
    [5]
    KIM J W, LEE D J. Optimized compact finite difference schemes with maximum resolution[J]. AIAA Journal, 1996, 34(5): 887-893.
    [6]
    张涵信. 无波动、无自由参数的耗散差分格式[J]. 空气动力学学报, 1988, 7(2) : 143-165.
    [7]
    JIANG G S, SHU C W. Efficient implementation of weighted ENO schemes[J]. Journal of Computational Physics, 1996, 126(1): 202-228.
    [8]
    DENG X G, ZHANG H X. Developing highorder weighted compact nonlinear schemes[J]. Journal of Computational Physics , 2000, 165(1): 22-44.
    [9]
    DENG X G. Highorder accurate dissipative weighted compact nonlinear schemes[J]. Science in China (Series A), 2002, 45(3): 356-370.
    [10]
    PIROZZOLI S. On the spectral properties of shockcapturing schemes[J]. Journal of Computational Physics, 2006, 219(2): 489-497.
    [11]
    NONOMURA T, IIZUKA N, FUJII K. Freestream and  vortex preservation properties of highorder WENO and WCNS on curvilinear grids[J]. Computers and Fluids, 2010, 39(2): 197-214.
    [12]
    DENG X G, MAO M L, TU G H, et al. Geometric conservation law and applications to highorder finite difference schemes with stationary grids[J]. Journal of Computational Physics, 2011, 230(4): 1100-1115.
    [13]
    DENG X G, MAO M L, TU G H, et al. Extending weighted compact nonlinear schemes to complex grids with characteristic based interface conditions[J]. AIAA Journal, 2010, 48(12): 2840-2851.
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