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A new class of central compact schemes with spectral-like resolution II: Hybrid weighted nonlinear schemes

Xuliang Liu China Aerodynamics Research and Development Center Shuhai Zhang China Aerodynamics Research and Development Center Hanxin Zhang China Aerodynamics Research and Development Center Chi-Wang Shu Brown University

Numerical Analysis and Scientific Computing mathscidoc:1610.25032

Journal of Computational Physics, 284, 133-154, 2015
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, S. Zhang, H. Zhang and C-W. Shu, A new class of central compact schemes with spectral-like resolution I: Linear schemes, Journal of Computational Physics 248 (2013) 235-256]. 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.
Compact scheme, WENO scheme, high resolution, low dissipation, weighted interpolation
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@inproceedings{xuliang2015a,
  title={A new class of central compact schemes with spectral-like resolution II: Hybrid weighted nonlinear schemes},
  author={Xuliang Liu, Shuhai Zhang, Hanxin Zhang, and Chi-Wang Shu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012034646733504150},
  booktitle={Journal of Computational Physics},
  volume={284},
  pages={133-154},
  year={2015},
}
Xuliang Liu, Shuhai Zhang, Hanxin Zhang, and Chi-Wang Shu. A new class of central compact schemes with spectral-like resolution II: Hybrid weighted nonlinear schemes. 2015. Vol. 284. In Journal of Computational Physics. pp.133-154. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012034646733504150.
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