Staggered discontinuous Galerkin methods for the incompressible NavierStokes equations

Siu Wun Cheung Tsz Shun Eric CHUNG Hyea Hyun Kim Yue Qian

Numerical Analysis and Scientific Computing mathscidoc:1910.43497

Journal of Computational Physics, 302, 251-266, 2015.12
In this paper, we present a staggered discontinuous Galerkin method for the approximation of the incompressible NavierStokes equations. Our new method combines the advantages of discontinuous Galerkin methods and staggered meshes, and results in many good properties, namely local and global conservations, optimal convergence and superconvergence through the use of a local postprocessing technique. Another key feature is that our method provides a skew-symmetric discretization of the convection term, with the aim of giving a better conservation property compared with existing discretizations. We will present extensive numerical results, including Kovasznay flow, Taylor vortex flow, lid-driven cavity flow, parallel plate flow and channel expansion flow, to show the performance of the method.
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@inproceedings{siu2015staggered,
  title={Staggered discontinuous Galerkin methods for the incompressible NavierStokes equations},
  author={Siu Wun Cheung, Tsz Shun Eric CHUNG, Hyea Hyun Kim, and Yue Qian},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020181024741477026},
  booktitle={Journal of Computational Physics},
  volume={302},
  pages={251-266},
  year={2015},
}
Siu Wun Cheung, Tsz Shun Eric CHUNG, Hyea Hyun Kim, and Yue Qian. Staggered discontinuous Galerkin methods for the incompressible NavierStokes equations. 2015. Vol. 302. In Journal of Computational Physics. pp.251-266. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020181024741477026.
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