Development of high-order weighted compact schemes with various difference methods
Development of high-order weighted compact schemes with various difference methods
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DOI：
10.1016/j.compfluid.2016.06.003
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发表时间：
2016-09
影响因子：
2.8
通讯作者：
Xuliang Liu;Shuhai Zhang;Hanxin Zhang
中科院分区：
文献类型：
--
作者：
Xuliang Liu;Shuhai Zhang;Hanxin Zhang
本文研究了基于线性中心紧致格式的高阶加权紧致格式的发展（Liu et al.，2013年）。为了捕捉强间断，将高阶迎风加权非线性插值与中心紧致格式和格心紧致格式相结合，得到两种不同的加权紧致格式，分别称为CCSSR-W和CCCSSR-W格式。将CCSSR-W格式发展到九阶，并详细研究了四种不同非线性权系数的CCSSR-W格式。作为CCSSR-HW方案的改进（Liu等人，2015），将混合加权非线性插值方法代入单元中心紧致格式，得到CCCSSR-HW格式.对于所有提出的格式，通量矢量分裂方法进行耦合与保守通量的特征投影。通过系统的精度检验、谱分析和数值试验，结果表明高阶CCSSR-W格式比低阶CCSSR-W格式精度更高、效果更好。CCCSSR-W方案比原韦诺方案具有更好的精度和分辨率。CCCSSR-HW格式比CCSSR-HW格式具有更高的分辨率和更低的功耗，甚至优于高阶CCSSR-W格式。
This paper is concerned with the development of high-order weighted compact schemes based on linear central compact schemes (Liu et al., 2013). For the purpose of capturing strong discontinuities, the high-order upwind weighted nonlinear interpolations are combined with the central compact schemes and cell-centered compact schemes to achieve two different weighted compact schemes, called the CCSSR-W and CCCSSR-W schemes respectively. The CCSSR-W schemes are developed up to ninth order, and four different nonlinear weights of CCSSR-W schemes are investigated in detail. As an improvement of the CCSSR-HW scheme (Liu et al., 2015), the hybrid weighted nonlinear interpolation is substituted into the cell-centered compact scheme to obtain the CCCSSR-HW scheme. For all the proposed schemes, the flux vector splitting method is carried out by coupling with characteristic projections on the conservative fluxes. Through the systematic accuracy tests, spectral analysis and numerical experiments, the results demonstrate that the higher order CCSSR-W scheme is more accurate and effective than the lower order ones. The CCCSSR-W scheme has better accuracy and resolution than the original WENO scheme. The CCCSSR-HW scheme has higher resolution and lower dissipation than the CCSSR-HW scheme, and even better than the higher order CCSSR-W schemes.