Development of nonlinear weighted compact schemes with increasingly higher order accuracy
Development of nonlinear weighted compact schemes with increasingly higher order accuracy
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开发具有越来越高阶精度的非线性加权紧凑方案
DOI：
10.1016/j.jcp.2008.04.012
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发表时间：
2008-07
期刊：
影响因子：
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中科院分区：
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本文设计了一类高精度的非线性加权紧致格式，它们是邓和张提出的非线性加权紧致格式的高阶推广[X.邓，H.Zhang，发展高阶加权紧致非线性格式，J.Comput。太棒了。165(2000)22-44]和江、舒的加权基本无振荡格式[G-S江，舒振文，加权ENO格式的有效实现，J.太棒了。126(1996)202-228]和Balsara和Shu[D.S.Balsara，C.-W.Shu，保单调性加权基本非振荡格式具有越来越高的精度阶，J.太棒了。160(2000)405-452]。这些非线性加权紧致格式是在Lele[S.K.Lele，具有类谱分辨率的紧致有限差分格式]的基础上提出的。太棒了。103(1992)16-42]。我们不像邓和张(2000)那样对保守变量进行非线性内插，而是直接在其模板上对通量进行内插。利用Lax-Friedrichs通量分裂和特征投影，所得到的内插公式与常规的WENO格式相似。因此，可以直接复制常规WENO格式的详细分析甚至许多代码片段。通过系统的试验和与常规WENO格式的比较，我们观察到非线性加权紧致格式具有相同的捕捉强不连续性的能力，同时提高了短波的分辨率，减少了数值耗散。
In this paper, we design a class of high order accurate nonlinear weighted compact schemes that are higher order extensions of the nonlinear weighted compact schemes proposed by Deng and Zhang [X. Deng, H. Zhang, Developing high-order weighted compact nonlinear schemes, J. Comput. Phys. 165 (2000) 22–44] and the weighted essentially non-oscillatory schemes of Jiang and Shu [G.-S. Jiang, C.-W. Shu, Efficient implementation of weighted ENO schemes, J. Comput. Phys. 126 (1996) 202–228] and Balsara and Shu [D.S. Balsara, C.-W. Shu, Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy, J. Comput. Phys. 160 (2000) 405–452]. These nonlinear weighted compact schemes are proposed based on the cell-centered compact scheme of Lele [S.K. Lele, Compact finite difference schemes with spectral-like resolution, J. Comput. Phys. 103 (1992) 16–42]. Instead of performing the nonlinear interpolation on the conservative variables as in Deng and Zhang (2000), we propose to directly interpolate the flux on its stencil. Using the Lax–Friedrichs flux splitting and characteristic-wise projection, the resulted interpolation formulae are similar to those of the regular WENO schemes. Hence, the detailed analysis and even many pieces of the code can be directly copied from those of the regular WENO schemes. Through systematic test and comparison with the regular WENO schemes, we observe that the nonlinear weighted compact schemes have the same ability to capture strong discontinuities, while the resolution of short waves is improved and numerical dissipation is reduced.
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DOI：
10.1137/1.9781611970425
发表时间：
1977
期刊：
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影响因子：
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作者：
D. Gottlieb;S. Orszag
通讯作者：
D. Gottlieb;S. Orszag
DOI：
10.1080/10618560108970024
发表时间：
2001-10
影响因子：
1.3
作者：
Li Jiang;H. Shan;Chaoqun Liu
通讯作者：
Li Jiang;H. Shan;Chaoqun Liu
DOI：
--
发表时间：
2001-08
期刊：
--
影响因子：
--
作者：
Li Jiang;H. Shan;Chaoqun Liu
通讯作者：
Li Jiang;H. Shan;Chaoqun Liu
DOI：
10.2514/6.2001-376
发表时间：
2001
期刊：
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影响因子：
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作者：
G. Constantinescu;S. Lele
通讯作者：
G. Constantinescu;S. Lele
影响因子：
4.1
作者：
R. Shukla;X. Zhong
通讯作者：
R. Shukla;X. Zhong