田奇, 郭元, 梁贤, 李新亮. 自适应的高精度中心-WENO混合格式[J]. 空气动力学学报, 2019, 37(4): 541-545, 577. DOI: 10.7638/kqdlxxb-2017.0050
引用本文: 田奇, 郭元, 梁贤, 李新亮. 自适应的高精度中心-WENO混合格式[J]. 空气动力学学报, 2019, 37(4): 541-545, 577. DOI: 10.7638/kqdlxxb-2017.0050
TIAN Qi, GUO Yuan, LIANG Xian, LI Xinliang. An adaptive high-resolution hybrid scheme using central flux scheme and WENO scheme[J]. ACTA AERODYNAMICA SINICA, 2019, 37(4): 541-545, 577. DOI: 10.7638/kqdlxxb-2017.0050
Citation: TIAN Qi, GUO Yuan, LIANG Xian, LI Xinliang. An adaptive high-resolution hybrid scheme using central flux scheme and WENO scheme[J]. ACTA AERODYNAMICA SINICA, 2019, 37(4): 541-545, 577. DOI: 10.7638/kqdlxxb-2017.0050

自适应的高精度中心-WENO混合格式

An adaptive high-resolution hybrid scheme using central flux scheme and WENO scheme

  • 摘要: 为对可压缩流动进行高精度高分辨率的数值模拟,基于模板的光滑度量函数,构造了新型的加权因子,在此基础上将7阶精度的WENO格式与8阶中心格式进行加权组合,构造了一种自适应低耗散的中心-WENO混合格式(H-WENO7-CD8),并采用Fourier方法对离散格式数学特性进行了理论分析。该自适应的高精度中心-WENO混合格式相比于七阶的WENO格式具有更小的耗散误差。通过对激波-密度干扰问题、Rayleigh-Taylor不稳定性问题和双Mach反射问题的数值模拟,并与WENO-JS格式的计算结果对比,结果表明:该格式结合了WENO格式和中心格式的特点,能更好地捕捉激波,对物理脉动也具有较高的分辨率,适合于复杂流体流动的数值模拟。

     

    Abstract: Aiming at high accuracy and high resolution computation for numerical simulation of compressible fluid flows, based on the smoothness measurement of the flux function of the stencil, the new kind of weighted factor is constructed. On the basis, the hybrid scheme (H-WENO7-CD8) combines the characteristics of WENO scheme and central flux scheme, and it improves the resolution of the scheme and the ability to capture the shock wave. The Fourier method is adopted to analysis the mathematical characteristics of the discrete scheme. The adaptive hybrid scheme has low dissipation. By the numerical simulation tests of the Shu-Osher shock-density interference problem, the two-dimensional Rayleigh-Taylor instability problem, and double Mach reflection, compared with the numerical tests of the WENO-JS scheme, the present hybrid scheme can capture the shock wave better, and it has higher resolution for shock waves and small-scale waves with a low computation cost. Therefore, the present scheme lays an algorithm foundation for high resolution numerical simulation of compressible fluid flows such as the shock wave-turbulent layer interaction problem or Richtmyer-Meshkov instability problem.

     

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