Resolution-optimised nonlinear scheme for secondary derivatives
Resolution-optimised nonlinear scheme for secondary derivatives
复制标题
二阶导数的分辨率优化非线性方案
DOI：
10.1080/10618562.2016.1164849
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发表时间：
2016-02
影响因子：
1.3
通讯作者：
Li Xinliang
中科院分区：
文献类型：
--
作者：
Li Li;Yu Changping;Chen Zhe;Li Xinliang
设计了二阶导数全波数范围内具有类谱分辨率的5点模板优化非线性格式。该方案弥补了传统线性方案的耗散不足，抑制了大涡模拟中常出现的高波数处的伪能量积累。新格式由一个线性四阶中心格式项和一个人工粘度项组成。这两项由一个非线性权值连接起来。所提出的非线性权值是基于傅里叶分析而不是泰勒分析来设计的，以保证类似光谱的分辨率。此外，新方案的精度不受优化的影响，达到了四阶精度。采用一维扩散问题、一维定常粘性伯格激波、二维涡旋衰减、三维各向同性衰减湍流和完全发育的湍流通道流动对新方案进行了数值验证。实验结果表明，新方案具有谱样分辨率，可以提高湍流能谱、耗散率和高阶统计量的精度。
A 5-point-stencil optimised nonlinear scheme with spectral-like resolution within the whole wave number range for secondary derivatives is devised. The proposed scheme can compensate for the dissipation deficiency of traditional linear schemes and suppress the spurious energy accumulation that occurs at high wave numbers, both of which are frequently encountered in large eddy simulation. The new scheme is composed of a linear fourth-order central scheme term and an artificial viscosity term. These two terms are connected by a nonlinear weight. The proposed nonlinear weight is designed based on Fourier analysis, rather than Taylor analysis, to guarantee a spectral-like resolution. Moreover, the accuracy is not affected by the optimisation, and the new scheme reaches fourth-order accuracy. The new scheme is tested numerically using the one-dimensional diffusion problem, one-dimensional steady viscous Burger’s shock, two-dimensional vortex decaying, three-dimensional isotropic decaying turbulence and fully developed turbulent channel flow. All the tests confirm that the new scheme has spectral-like resolution and can improve the accuracy of the energy spectrum, dissipation rate and high-order statistics of turbulent flows.
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DOI：
10.1016/j.jcp.2007.09.020
发表时间：
2008
期刊：
J. Comput. Phys.
影响因子：
--
作者：
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通讯作者：
C. Kennedy;A. Gruber
DOI：
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发表时间：
1923-10
期刊：
Philosophical Magazine Series 1
影响因子：
--
作者：
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通讯作者：
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影响因子：
4.1
作者：
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通讯作者：
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DOI：
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发表时间：
2008-06
期刊：
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影响因子：
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作者：
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通讯作者：
Yiqing Shen;Gecheng Zha;Xiangying Chen
影响因子：
4.1
作者：
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通讯作者：
D. Fu;Yanwen Ma