Staggered discontinuous Galerkin approximation for immersed boundary method

SW Cheung Tsz Shun Eric CHUNG HH Kim

Numerical Analysis and Scientific Computing mathscidoc:1910.43580

arXiv preprint arXiv:1609.01046, 2016.9
In this paper, we present a staggered discontinuous Galerkin immersed boundary method (SDGIBM) for the numerical approximation of fluid-structure interaction. The immersed boundary method is used to model the fluid-structure interaction, while the fluid flow is governed by incompressible Navier-Stokes equations. One advantage of using Galerkin method over the finite difference method with immersed boundary method is that we can avoid approximations of the Dirac Delta function. Another key ingredient of our method is that our solver for incompressible Navier-Stokes equations combines the advantages of discontinuous Galerkin methods and staggered meshes, and results in many good properties, namely local and global conservations and pointwise divergence-free velocity field by a local postprocessing technique. Furthermore, energy stability is improved by a skew-symmetric discretization of the convection term. We will present numerical results to show the performance of the method.
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@inproceedings{sw2016staggered,
  title={Staggered discontinuous Galerkin approximation for immersed boundary method},
  author={SW Cheung, Tsz Shun Eric CHUNG, and HH Kim},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020202941665167109},
  booktitle={arXiv preprint arXiv:1609.01046},
  year={2016},
}
SW Cheung, Tsz Shun Eric CHUNG, and HH Kim. Staggered discontinuous Galerkin approximation for immersed boundary method. 2016. In arXiv preprint arXiv:1609.01046. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020202941665167109.
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