A new class of central compact schemes with spectral-like resolution I: Linear 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:1610.25057

Journal of Computational Physics, 248, 235-256, 2013
In this paper, we design a new class of central compact schemes based on the cell-centered compact schemes of Lele {[}S.K. Lele, Compact finite difference schemes with spectral-like resolution, J. Comput. Phys. 103 (1992) 16-42{]}. These schemes equate a weighted sum of the nodal derivatives of a smooth function to a weighted sum of the function on both the grid points (cell boundaries) and the cell-centers. In our approach, instead of using a compact interpolation to compute the values on cell-centers, the physical values on these half grid points are stored as independent variables and updated using the same scheme as the physical values on the grid points. This approach increases the memory requirement but not the computational costs. Through systematic Fourier analysis and numerical tests, we observe that the schemes have excellent properties of high order, high resolution and low dissipation. It is an ideal class of schemes for the simulation of multi-scale problems such as aeroacoustics and turbulence.
Compact scheme, high resolution, direct numerical simulation, computational aeroacoustics
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@inproceedings{xuliang2013a,
  title={A new class of central compact schemes with spectral-like resolution I: Linear schemes},
  author={Xuliang Liu, Shuhai Zhang, Hanxin Zhang, and Chi-Wang Shu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012060550930093175},
  booktitle={Journal of Computational Physics},
  volume={248},
  pages={235-256},
  year={2013},
}
Xuliang Liu, Shuhai Zhang, Hanxin Zhang, and Chi-Wang Shu. A new class of central compact schemes with spectral-like resolution I: Linear schemes. 2013. Vol. 248. In Journal of Computational Physics. pp.235-256. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012060550930093175.
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