A new class of central compact schemes with spectral-like resolution II: Hybrid weighted nonlinear schemes
A new class of central compact schemes with spectral-like resolution II: Hybrid weighted nonlinear schemes
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具有类谱分辨率的新型中心紧凑方案 II：混合加权非线性方案
DOI：
10.1016/j.jcp.2014.12.027
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发表时间：
2015
影响因子：
4.1
通讯作者：
Chi-Wang Shu
中科院分区：
文献类型：
--
作者：
Xuliang Liu;Shuhai Zhang;Hanxin Zhang;Chi-Wang Shu
本文在已有的线性中心紧致格式的基础上，发展了一类具有类谱分辨率的非线性紧致格式（X。Liu等人，2013 [20]）。在我们的方法中，我们计算单元节点上的通量导数的单元节点上的物理通量和单元中心的数值通量。为了获得单元中心的数值通量，我们执行一个迎风插值和中心插值的加权混合插值。通过系统的分析和数值试验，我们表明我们的非线性紧致格式具有高阶、高分辨率和低耗散的特点，并且具有与规则加权基本无振荡（韦诺）格式相同的捕捉强间断的能力。这是一个很好的选择，模拟多尺度问题的冲击波。
In this paper, we develop a class of nonlinear compact schemes based on our previous linear central compact schemes with spectral-like resolution (X. Liu et al., 2013 [20]). In our approach, we compute the flux derivatives on the cell-nodes by the physical fluxes on the cell nodes and numerical fluxes on the cell centers. To acquire the numerical fluxes on the cell centers, we perform a weighted hybrid interpolation of an upwind interpolation and a central interpolation. Through systematic analysis and numerical tests, we show that our nonlinear compact scheme has high order, high resolution and low dissipation, and has the same ability to capture strong discontinuities as regular weighted essentially non-oscillatory (WENO) schemes. It is a good choice for the simulation of multiscale problems with shock waves.