Stability analysis of the inverse Lax-Wendroff boundary treatment for high order upwind-biased finite difference schemes

Tingting Li University of Science and Technology of China Chi-Wang Shu Brown University Mengping Zhang University of Science and Technology of China

Numerical Analysis and Scientific Computing mathscidoc:1610.25016

Journal of Computational and Applied Mathematics, 299, 140-158, 2016
In this paper, we consider linear stability issues for one-dimensional hyperbolic conservation laws using a class of conservative high order upwind-biased finite difference schemes, which is a prototype for the weighted essentially non-oscillatory (WENO) schemes, for initial-boundary value problems (IBVP). The inflow boundary is treated by the so-called inverse Lax-Wendroff (ILW) or simplified inverse Lax-Wendroff (SILW) procedure, and the outflow boundary is treated by the classical high order extrapolation. A third order total variation diminishing (TVD) Runge-Kutta time discretization is used in the fully discrete case. Both GKS (Gustafsson, Kreiss and Sundstr\"om) and eigenvalue analysis are performed for both semi-discrete and fully discrete schemes. The two different analysis techniques yield consistent results. Numerical tests are performed to demonstrate the stability results predicted by the analysis.
high order upwind-biased schemes; inverse Lax-Wendroff procedure; simplified inverse Lax-Wendroff procedure; extrapolation; stability; GKS theory; eigenvalue analysis
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@inproceedings{tingting2016stability,
  title={Stability analysis of the inverse Lax-Wendroff boundary treatment for high order upwind-biased finite difference schemes},
  author={Tingting Li, Chi-Wang Shu, and Mengping Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161011104841063897130},
  booktitle={Journal of Computational and Applied Mathematics},
  volume={299},
  pages={140-158},
  year={2016},
}
Tingting Li, Chi-Wang Shu, and Mengping Zhang. Stability analysis of the inverse Lax-Wendroff boundary treatment for high order upwind-biased finite difference schemes. 2016. Vol. 299. In Journal of Computational and Applied Mathematics. pp.140-158. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161011104841063897130.
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