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一种面向激波噪声计算的加权优化紧致格式及非线性效应分析

李虎 罗勇 刘旭亮 武从海 韩帅斌 王益民

李虎, 罗勇, 刘旭亮, 武从海, 韩帅斌, 王益民. 一种面向激波噪声计算的加权优化紧致格式及非线性效应分析. 力学学报, 2022, 54(10): 2747-2759 doi: 10.6052/0459-1879-22-254
引用本文: 李虎, 罗勇, 刘旭亮, 武从海, 韩帅斌, 王益民. 一种面向激波噪声计算的加权优化紧致格式及非线性效应分析. 力学学报, 2022, 54(10): 2747-2759 doi: 10.6052/0459-1879-22-254
Li Hu, Luo Yong, Liu Xuliang, Wu Conghai, Han Shuaibin, Wang Yimin. A weighted-optimization compact scheme for shock-associated noise computation and its nonlinear effect analysis. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(10): 2747-2759 doi: 10.6052/0459-1879-22-254
Citation: Li Hu, Luo Yong, Liu Xuliang, Wu Conghai, Han Shuaibin, Wang Yimin. A weighted-optimization compact scheme for shock-associated noise computation and its nonlinear effect analysis. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(10): 2747-2759 doi: 10.6052/0459-1879-22-254

一种面向激波噪声计算的加权优化紧致格式及非线性效应分析

doi: 10.6052/0459-1879-22-254
基金项目: 国家自然科学基金(11732016, 11972360, 12172374, 12102450)、四川省科技计划(2018JZ0076)、中国空气动力研究与发展中心基础和前沿技术研究基金(PJD20200185)和国家数值风洞工程资助项目
详细信息
    作者简介:

    李虎, 助理研究员, 主要研究方向: 计算气动声学、高精度数值方法. E-mail: lihu@cardc.cn

  • 中图分类号: V211.3, O354.3

A WEIGHTED-OPTIMIZATION COMPACT SCHEME FOR SHOCK-ASSOCIATED NOISE COMPUTATION AND ITS NONLINEAR EFFECT ANALYSIS

  • 摘要: 在超声速流动中, 激波与湍流结构的相互作用会产生高强度的激波噪声. 激波噪声的高保真计算要求激波捕捉格式具有高阶精度、低耗散和低色散特性, 同时还要尽可能地减弱格式的非线性效应. 现有的六阶精度迎风/对称混合型加权非线性紧致格式CCSSR-HW-6在基于对称模板构造网格中心处的数值通量时引入了两级加权, 且两级加权都需要构造非线性的权系数, 因而非线性效应较强. 本文以修正波数的误差积分函数为优化目标函数, 优化了CCSSR-HW-6格式的非线性特性, 建立了加权优化紧致格式WOCS. 精度验证表明WOCS格式的精度高于5阶. 谱特性分析表明, 与原方法相比, WOCS格式的耗散误差和非线性效应显著降低. 典型激波噪声问题数值实验表明: WOCS格式不仅提高了对高频波的分辨能力, 而且显著地消除了数值解中因格式的非线性效应所导致的非物理振荡.

     

  • 图  1  迎风/对称混合型加权非线性紧致格式的构造模板

    Figure  1.  Candidate stencils of hybrid upwind/symmetric weighted nonlinear compact scheme

    图  2  修正波数的线性响应部分

    Figure  2.  The linear response part of the modified wavenumber

    图  3  修正波数的非线性响应部分

    Figure  3.  The nonlinear response part of the modified wavenumber

    图  4  激波−声波相互作用问题的数值结果

    Figure  4.  Numerical results of shock-sound interaction problem

    图  5  Titarev-Toro问题的数值结果

    Figure  5.  Numerical results of Titarev-Toro problem

    图  6  激波−涡量波相互作用在t = 0.2时刻的涡量空间分布

    Figure  6.  The spatial distribution of vorticity in the shock-vorticity wave interaction at t = 0.2

    图  7  激波−涡量波相互作用在t = 0.2时刻沿直线y = 0的涡量分布

    Figure  7.  The vorticity distribution along the line y = 0 in the shock-vorticity wave interaction at t = 0.2

    图  8  激波−强旋涡相互作用在t = 10时刻的胀量场

    Figure  8.  The dilatation field of shock-strong vortex interaction at t = 10

    图  9  激波−强旋涡相互作用在t = 10时刻的胀量和数值阴影沿径向的分布

    Figure  9.  The radial distribution of dilatation and numerical shadowgraph in shock-strong vortex interaction at t = 10

    图  10  激波−强旋涡相互作用在t = 10时刻的数值阴影

    Figure  10.  Numerical shadowgraph of shock-strong vortex interaction at t = 10

    表  1  加权优化紧致格式的数值误差和精度阶数

    Table  1.   Numerical errors and accuracy order of the weighted optimization compact scheme

    NL1 errorL1 orderL errorL order
    102.868 × 10−34.414 × 10−3
    205.357 × 10−55.748.480 × 10−55.70
    401.029 × 10−65.701.619 × 10−65.71
    802.156 × 10−85.583.391 × 10−85.58
    1605.093 × 10−105.408.003 × 10−105.40
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-06-07
  • 录用日期:  2022-07-13
  • 网络出版日期:  2022-07-14
  • 刊出日期:  2022-10-18

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