Robust high order discontinuous Galerkin schemes for two-dimensional gaseous detonations

Cheng Wang Beijing Institute of Technology Xiangxiong Zhang Brown University Chi-Wang Shu Brown University Jianguo Ning Beijing Institute of Technology

Numerical Analysis and Scientific Computing mathscidoc:1610.25080

Journal of Computational Physics, 231, 653-665, 2012
One of the main challenges in computational simulations of gas detonation propagation is that negative density or negative pressure may emerge during the time evolution, which will cause blow-ups. Therefore, schemes with provable positivity-preserving of density and pressure are desired. First order and second order positivity-preserving schemes were well studied. For high order discontinuous Galerkin (DG) method, even though the characteristicwise TVB limiter can kill oscillations, it is not sufficient to maintain the positivity. A simple solution for arbitrarily high order positivity-preserving schemes solving Euler equations was proposed recently. In this paper, we first discuss an extension of the technique to design arbitrarily high order positivity-preserving DG schemes for reactive Euler equations. We then present a simpler and more robust implementation of the positivity-preserving limiter than the one before. Numerical tests, including very demanding examples in gaseous detonations, indicate that the third order DG scheme with the new positivity-preserving limiter produces satisfying results even without the TVB limiter.
discontinuous Galerkin method; positivity preserving; high order accuracy; gaseous detonations
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@inproceedings{cheng2012robust,
  title={Robust high order discontinuous Galerkin schemes for two-dimensional gaseous detonations},
  author={Cheng Wang, Xiangxiong Zhang, Chi-Wang Shu, and Jianguo Ning},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012114417679904198},
  booktitle={Journal of Computational Physics},
  volume={231},
  pages={653-665},
  year={2012},
}
Cheng Wang, Xiangxiong Zhang, Chi-Wang Shu, and Jianguo Ning. Robust high order discontinuous Galerkin schemes for two-dimensional gaseous detonations. 2012. Vol. 231. In Journal of Computational Physics. pp.653-665. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012114417679904198.
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