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Volume 14, Issue 4
A Hybrid WENO Method with Modified Ghost Fluid Method for Compressible Two-Medium Flow Problems

Zhuang Zhao, Yibing Chen & Jianxian Qiu

Numer. Math. Theor. Meth. Appl., 14 (2021), pp. 972-997.

Published online: 2021-09

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  • Abstract

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.

  • AMS Subject Headings

65M60, 35L65

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-14-972, author = {Zhao , ZhuangChen , Yibing and Qiu , Jianxian}, title = {A Hybrid WENO Method with Modified Ghost Fluid Method for Compressible Two-Medium Flow Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2021}, volume = {14}, number = {4}, pages = {972--997}, abstract = {

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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2020-0190}, url = {http://global-sci.org/intro/article_detail/nmtma/19526.html} }
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 -

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.

Zhuang Zhao, Yibing Chen & Jianxian Qiu. (2021). A Hybrid WENO Method with Modified Ghost Fluid Method for Compressible Two-Medium Flow Problems. Numerical Mathematics: Theory, Methods and Applications. 14 (4). 972-997. doi:10.4208/nmtma.OA-2020-0190
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