On the spectral properties of shock-capturing schemes
On the spectral properties of shock-capturing schemes
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DOI：
10.1016/j.jcp.2006.07.009
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发表时间：
2006-12
期刊：
影响因子：
--
通讯作者：
S. Pirozzoli
中科院分区：
文献类型：
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作者：
S. Pirozzoli
在这篇短文中，我们分析了波数空间中的非线性激波捕捉方案的性能。为此，我们提出了一种新的近似色散关系表示法，它解释了非线性效应的先导阶。给出了几个例子，证实了与传统的表示法相比，本理论对真实解行为的定性表示有了改进。该理论可为具体应用选择最具成本效益的方案提供有益的指导，并可为优化方案的开发提供依据。
In this short note we analyze the performance of nonlinear, shock-capturing schemes in wavenumber space. For this purpose we propose a new representation for the approximate dispersion relation which accounts to leading order for nonlinear effects. Several examples are presented, which confirm that the present theory yields an improved qualitative representation of the true solution behavior compared to conventional representations. The theory can provide useful guidance for the choice of the most cost-effective schemes for specific applications, and may constitute a basis for the development of optimized ones.