TY - JOUR
T1 - A Hybrid WENO Method with Modified Ghost Fluid Method for Compressible Two-Medium Flow Problems
AU - Zhao , Zhuang
AU - Chen , Yibing
AU - Qiu , Jianxian
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 972
EP - 997
PY - 2021
DA - 2021/09
SN - 14
DO - http://doi.org/10.4208/nmtma.OA-2020-0190
UR - https://global-sci.org/intro/article_detail/nmtma/19526.html
KW - Hybrid WENO scheme, two-medium flow problems, modified ghost fluid method,
zero point existence theorem.
AB - <p style="text-align: justify;">In this paper, we develop a simplified hybrid weighted essentially non-oscillatory (WENO) method combined with the modified ghost fluid method (MGFM)
[31] to simulate the compressible two-medium flow problems. The MGFM can turn
the two-medium flow problems into two single-medium cases by defining the ghost
fluids state in terms of the predicted the interface state, which makes the material
interface “invisible”. For the single medium flow case, we adapt between the linear
upwind scheme and the WENO scheme automatically by identifying the regions of
the extreme points for the reconstruction polynomial as same as the hybrid WENO
scheme [55]. Instead of calculating their exact locations, we only need to know the
regions of the extreme points based on the zero point existence theorem, which is
simpler for implementation and saves computation time. Meanwhile, it still keeps
the robustness and has high efficiency. Extensive numerical results for both one
and two dimensional two-medium flow problems are performed to demonstrate the
good performances of the proposed method.</p>