High order finite difference methods with subcell resolution for stiff multispecies detonation capturing

Wei Wang Florida International University Chi-Wang Shu Brown University H. C. Yee NASA Ames Research Center Dmitry V. Kotov Stanford University Bjorn Sjogreen Lawrence Livermore National Laboratory

Numerical Analysis and Scientific Computing mathscidoc:1610.25035

Communications in Computational Physics, 17, 317-336, 2015
In this paper, we extend the high order finite-difference method with subcell resolution (SR) for two-species stiff one-reaction models to multispecies and multireaction chemical reactive flows, which are significantly more difficult because of the multiple scales generated by different reactions. For reaction problems, when the reaction time scale is very small, the reaction zone scale is also small and the governing equations become very stiff. Wrong propagation speed of discontinuity may occur due to the underresolved numerical solution in both space and time. The present SR method for reactive Euler system is a fractional step method. In the convection step, any high order shock-capturing method can be used. In the reaction step, an ODE solver is applied but with certain computed flow variables in the shock region modified by the Harten subcell resolution idea. Several numerical examples of multispecies and multireaction reactive flows are performed in both one and two dimensions. Studies demonstrate that the SR method can capture the correct propagation speed of discontinuities in very coarse meshes.
stiff reaction term, shock capturing, detonation, WENO, ENO subcell resolution, multispecies, multireactions
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@inproceedings{wei2015high,
  title={High order finite difference methods with subcell resolution for stiff multispecies detonation capturing},
  author={Wei Wang, Chi-Wang Shu, H. C. Yee, Dmitry V. Kotov, and Bjorn Sjogreen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012040326017112153},
  booktitle={Communications in Computational Physics},
  volume={17},
  pages={317-336},
  year={2015},
}
Wei Wang, Chi-Wang Shu, H. C. Yee, Dmitry V. Kotov, and Bjorn Sjogreen. High order finite difference methods with subcell resolution for stiff multispecies detonation capturing. 2015. Vol. 17. In Communications in Computational Physics. pp.317-336. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012040326017112153.
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