Numerical study on the convergence to steady state solutions of a new class of high order WENO schemes

Jun Zhu Chi-Wang Shu Brown University

Numerical Analysis and Scientific Computing mathscidoc:1804.25017

Journal of Computational Physics, 349, 80-96, 2017
A new class of high order weighted essentially non-oscillatory (WENO) schemes [J. Comput. Phys., 318 (2016), 110-121] is applied to solve Euler equations with steady state solutions. It is known that the classical WENO schemes [J. Comput. Phys., 126 (1996), 202-228] might suffer from slight post-shock oscillations. Even though such post-shock oscillations are small enough in magnitude and do not visually affect the essentially non-oscillatory property, they are truly responsible for the residue to hang at a truncation error level instead of converging to machine zero. With the application of this new class of WENO schemes, such slight post-shock oscillations are essentially removed and the residue can settle down to machine zero in steady state simulations. This new class of WENO schemes uses a convex combination of a quartic polynomial with two linear polynomials on unequal size spatial stencils in one dimension and is extended to two dimensions in a dimension-by-dimension fashion. By doing so, such WENO schemes use the same information as the classical WENO schemes in [J. Comput. Phys., 126 (1996), 202-228] and yield the same formal order of accuracy in smooth regions, yet they could converge to steady state solutions with very tiny residue close to machine zero for our extensive list of test problems including shocks, contact discontinuities, rarefaction waves or their interactions, and with these complex waves passing through the boundaries of the computational domain.
WENO scheme, unequal size spatial stencil, steady state solution
[ Download ] [ 2018-04-16 10:30:17 uploaded by chiwangshu ] [ 819 downloads ] [ 0 comments ]
@inproceedings{jun2017numerical,
  title={Numerical study on the convergence to steady state solutions of a new class of high order WENO schemes},
  author={Jun Zhu, and Chi-Wang Shu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180416103017970807052},
  booktitle={Journal of Computational Physics},
  volume={349},
  pages={80-96},
  year={2017},
}
Jun Zhu, and Chi-Wang Shu. Numerical study on the convergence to steady state solutions of a new class of high order WENO schemes. 2017. Vol. 349. In Journal of Computational Physics. pp.80-96. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180416103017970807052.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved