Analyses of the Dispersion Overshoot and Inverse Dissipation of the High-Order Finite Difference Scheme
Analyses of the Dispersion Overshoot and Inverse Dissipation of the High-Order Finite Difference Scheme
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高阶有限差分格式的色散超调和逆耗散分析
DOI：
10.1017/s2070073300001247
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发表时间：
2013-12
影响因子：
1.4
通讯作者：
Hanxin Zhang
中科院分区：
文献类型：
--
作者：
Qin Li;Qilong Guo;Hanxin Zhang
利用傅立叶变换和精度分析方法对高阶差分格式的色散超调和逆耗散进行了分析。讨论中的方案包括逐点和交错网格类型，并以加权形式使用三阶精度和三点模板的候选方案。所有这些都是构造差分格式的常用方法。提出了色散超调的判据，并讨论了它们的临界状态。两种类型的不稳定性进行了研究，由于逆耗散，特别是那些发生在较低的波数。提出了两种不稳定性发生的判据，并讨论了它们之间的关系。将解析结果与典型方案的傅立叶变换频散/耗散关系进行了比较。作为一个例子，给出了该准则在Weirs & Martin三阶格式中逆耗散修正的应用。
Analyses were performed on the dispersion overshoot and inverse dissipation of the high-order finite difference scheme using Fourier and precision analysis. Schemes under discussion included the pointwise- and staggered-grid type, and were presented in weighted form using candidate schemes with third-order accuracy and three-point stencil. All of these were commonly used in the construction of difference schemes. Criteria for the dispersion overshoot were presented and their critical states were discussed. Two kinds of instabilities were studied due to inverse dissipation, especially those that occur at lower wave numbers. Criteria for the occurrence were presented and the relationship of the two instabilities was discussed. Comparisons were made between the analytical results and the dispersion/dissipation relations by Fourier transformation of typical schemes. As an example, an application of the criteria was given for the remedy of inverse dissipation in Weirs & Martin’s third-order scheme.
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DOI：
10.1137/1.9781611970876
发表时间：
1987
期刊：
--
影响因子：
--
作者：
R. Vichnevetsky;J. Bowles
通讯作者：
R. Vichnevetsky;J. Bowles
DOI：
10.1016/j.jcp.2006.05.009
发表时间：
2006-12
期刊：
J. Comput. Phys.
影响因子：
--
作者：
M. Martín;Ellen M. Taylor;Minwei Wu;V. Weirs
通讯作者：
M. Martín;Ellen M. Taylor;Minwei Wu;V. Weirs
影响因子：
4.1
作者：
Xiaogang Deng;H. Maekawa
通讯作者：
Xiaogang Deng;H. Maekawa
影响因子：
4.1
作者：
LELE, SK
通讯作者：
LELE, SK
影响因子：
4.1
作者：
N. Adams;K. Shariff
通讯作者：
N. Adams;K. Shariff