Development and stability analysis of the inverse Lax-Wendroff boundary treatment for central compact schemes

Francois Vilar Brown University Chi-Wang Shu Brown University

Numerical Analysis and Scientific Computing mathscidoc:1610.25036

ESAIM: Mathematical Modelling and Numerical Analysis, 49, 39-67, 2015
In this paper, we generalize the so-called inverse Lax-Wendroff boundary treatment \cite{ilw} for the inflow boundary of a linear hyperbolic problem discretized by the recently introduced central compact schemes. The outflow boundary is treated by the classical extrapolation and a stability analysis for the resulting scheme is provided. To ensure the stability of the considered schemes provided with the chosen boundaries, the G-K-S theory is used, first in the semidiscrete case then in the fully discrete case with the third-order TVD Runge-Kutta time discretization. Afterwards, due to the high algebraic complexity of the G-K-S theory, the stability is analyzed by visualizing the eigenspectrum of the discretized operators. We show in this paper that the results obtained with these two different approaches are perfectly consistent. We also illustrate the high accuracy of the presented schemes on simple test problems.
Central compact schemes, initial boundary value problem, inverse Lax-Wendroff, extrapolation, G-K-S theory, eigenvalue spectrum
[ Download ] [ 2016-10-12 04:07:49 uploaded by chiwangshu ] [ 560 downloads ] [ 0 comments ] [ Cited by 6 ]
@inproceedings{francois2015development,
  title={ Development and stability analysis of the inverse Lax-Wendroff boundary treatment for central compact schemes},
  author={Francois Vilar, and Chi-Wang Shu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012040749596729154},
  booktitle={ESAIM: Mathematical Modelling and Numerical Analysis},
  volume={49},
  pages={39-67},
  year={2015},
}
Francois Vilar, and Chi-Wang Shu. Development and stability analysis of the inverse Lax-Wendroff boundary treatment for central compact schemes. 2015. Vol. 49. In ESAIM: Mathematical Modelling and Numerical Analysis. pp.39-67. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012040749596729154.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved