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A high order discontinuous Galerkin method for incompressible flows

Jian-Guo Liu University of Maryland Chi-Wang Shu Brown University

Numerical Analysis and Scientific Computing mathscidoc:1702.25060

Journal of Computational Physics, 160, (2), 577–596, 2000.5
In this paper we introduce a high-order discontinuous Galerkin method for two-dimensional incompressible flow in the vorticity stream-function formulation. The momentum equation is treated explicitly, utilizing the efficiency of the discontinuous Galerkin method. The stream function is obtained by a standard Poisson solver using continuous finite elements. There is a natural matching between these two finite element spaces, since the normal component of the velocity field is continuous across element boundaries. This allows for a correct upwinding gluing in the discontinuous Galerkin framework, while still maintaining total energy conservation with no numerical dissipation and total enstrophy stability. The method is efficient for inviscid or high Reynolds number flows. Optimal error estimates are proved and verified by numerical experiments.
incompressible flow; discontinuous Galerkin; high-order accuracy.
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@inproceedings{jian-guo2000a,
  title={A high order discontinuous Galerkin method for incompressible flows},
  author={Jian-Guo Liu, and Chi-Wang Shu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209114615078951391},
  booktitle={Journal of Computational Physics},
  volume={160},
  number={2},
  pages={577–596},
  year={2000},
}
Jian-Guo Liu, and Chi-Wang Shu. A high order discontinuous Galerkin method for incompressible flows. 2000. Vol. 160. In Journal of Computational Physics. pp.577–596. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209114615078951391.
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