An efficient implementation of the divergence free constraint in a discontinuous Galerkin method for magnetohydrodynamics on unstructured meshes

Christian Klingenberg University of Würzburg Frank Pörner University of Würzburg Yinhua Xia University of Science and Technology of China

Numerical Analysis and Scientific Computing mathscidoc:1612.25005

Communication in Computational Physic, 21, (2), 423-442, 2016.6
In this paper we consider a discontinuous Galerkin discretization of the ideal magnetohydrodynamics (MHD) equations on unstructured meshes, and the divergence free constraint ($\nabla \cdot \B = 0$) of its magnetic field $\B$. We first present two approaches for maintaining the divergence free constraint, namely the approach of a locally divergence free projection inspired by locally divergence free elements \cite{Li2005}, and another approach of the divergence cleaning technique given by Dedner et al. \cite{Dedner2002}. By combining these two approaches we obtain a efficient method at the almost same numerical cost. Finally, numerical experiments are performed to show the capacity and efficiency of the scheme.
Ideal magnetohydrodynamics equations, discontinuous Galerkin method, divergence free constraint, locally divergence free projection, divergence free cleaning technique.
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@inproceedings{christian2016an,
  title={An efficient implementation of the divergence free constraint in a discontinuous Galerkin method for magnetohydrodynamics on unstructured meshes},
  author={Christian Klingenberg, Frank Pörner, and Yinhua Xia},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161231214325386528701},
  booktitle={Communication in Computational Physic},
  volume={21},
  number={2},
  pages={423-442},
  year={2016},
}
Christian Klingenberg, Frank Pörner, and Yinhua Xia. An efficient implementation of the divergence free constraint in a discontinuous Galerkin method for magnetohydrodynamics on unstructured meshes. 2016. Vol. 21. In Communication in Computational Physic. pp.423-442. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161231214325386528701.
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