Compact High-Order Accurate Nonlinear Schemes
Compact High-Order Accurate Nonlinear Schemes
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DOI：
10.1006/jcph.1996.5553
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发表时间：
1997
影响因子：
4.1
通讯作者：
Xiaogang Deng;H. Maekawa
中科院分区：
文献类型：
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作者：
Xiaogang Deng;H. Maekawa
我们在这里开发紧凑的高阶精度非线性格式捕捉间断。这种格式通过采用单元中心紧致格式实现了高阶空间精度。紧凑的自适应插值的变量在细胞边缘的设计，自动“跳”到当地的不连续性。这是使整体紧致格式以无振荡的方式捕捉间断的关键。分析表明，在单元边缘设计紧凑插值的基本原则是避免插值与不连续数据相交，使得基于泰勒级数展开的精度分析在所有网格点上都是有效的。高阶龙格？时间积分采用库塔法。讨论了守恒性和边界格式。我们还将该方案推广到一个守恒律系统。多维问题的扩展是直接的。给出了一些典型的一维数值算例，包括激波管问题、强激波与复杂波的相互作用以及激波与湍流的相互作用。
We develop here compact high-order accurate nonlinear schemes for discontinuities capturing. Such schemes achieve high-order spatial accuracy by the cell-centered compact schemes. Compact adaptive interpolations of variables at cell edges are designed which automatically “jump” to local ones as discontinuities being encountered. This is the key to make the overall compact schemes capture discontinuities in a nonoscillatory manner. The analysis shows that the basic principle to design a compact interpolation of variables at the cell edges is to prevent it from crossing the discontinuous data, such that the accuracy analysis based on Taylor series expanding is valid over all grid points. A high-order Runge?Kutta method is employed for the time integration. The conservative property, as well as the boundary schemes, is discussed. We also extend the schemes to a system of conservation laws. The extensions to multidimensional problems are straightforward. Some typical one-dimensional numerical examples, including the shock tube problem, strong shock waves with complex wave interactions, and “shock/turbulence” interaction, are presented.