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Volume 30, Issue 3
A Hermite WENO Method with Modified Ghost Fluid Method for Compressible Two-Medium Flow Problems

Zhuang Zhao, Yong-Tao Zhang, Yibing Chen & Jianxian Qiu

Commun. Comput. Phys., 30 (2021), pp. 851-873.

Published online: 2021-07

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  • Abstract

In this paper, we develop a novel approach by combining a new robust finite difference Hermite weighted essentially non-oscillatory (HWENO) method [51] with the modified ghost fluid method (MGFM) [25] to simulate the compressible two-medium flow problems. The main idea is that we first use the technique of the MGFM to transform a two-medium flow problem to two single-medium cases by defining the ghost fluids status based on the predicted interface status. Then the efficient and robust HWENO finite difference method is applied for solving the single-medium flow cases. By using immediate neighbor information to deal with both the solution and its derivatives, the fifth order finite difference HWENO scheme adopted in this paper is more compact and has higher resolution than the classical fifth order finite difference WENO scheme of Jiang and Shu [14]. Furthermore, by combining the HWENO scheme with the MGFM to simulate the two-medium flow problems, less ghost point information is needed than that in using the classical WENO scheme in order to obtain the same numerical accuracy. Various one-dimensional and two-dimensional two-medium flow problems are solved to illustrate the good performances of the proposed method.

  • AMS Subject Headings

65M60, 35L65

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-30-851, author = {Zhao , ZhuangZhang , Yong-TaoChen , Yibing and Qiu , Jianxian}, title = {A Hermite WENO Method with Modified Ghost Fluid Method for Compressible Two-Medium Flow Problems}, journal = {Communications in Computational Physics}, year = {2021}, volume = {30}, number = {3}, pages = {851--873}, abstract = {

In this paper, we develop a novel approach by combining a new robust finite difference Hermite weighted essentially non-oscillatory (HWENO) method [51] with the modified ghost fluid method (MGFM) [25] to simulate the compressible two-medium flow problems. The main idea is that we first use the technique of the MGFM to transform a two-medium flow problem to two single-medium cases by defining the ghost fluids status based on the predicted interface status. Then the efficient and robust HWENO finite difference method is applied for solving the single-medium flow cases. By using immediate neighbor information to deal with both the solution and its derivatives, the fifth order finite difference HWENO scheme adopted in this paper is more compact and has higher resolution than the classical fifth order finite difference WENO scheme of Jiang and Shu [14]. Furthermore, by combining the HWENO scheme with the MGFM to simulate the two-medium flow problems, less ghost point information is needed than that in using the classical WENO scheme in order to obtain the same numerical accuracy. Various one-dimensional and two-dimensional two-medium flow problems are solved to illustrate the good performances of the proposed method.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0184}, url = {http://global-sci.org/intro/article_detail/cicp/19319.html} }
TY - JOUR T1 - A Hermite WENO Method with Modified Ghost Fluid Method for Compressible Two-Medium Flow Problems AU - Zhao , Zhuang AU - Zhang , Yong-Tao AU - Chen , Yibing AU - Qiu , Jianxian JO - Communications in Computational Physics VL - 3 SP - 851 EP - 873 PY - 2021 DA - 2021/07 SN - 30 DO - http://doi.org/10.4208/cicp.OA-2020-0184 UR - https://global-sci.org/intro/article_detail/cicp/19319.html KW - Hermite WENO scheme, two-medium flow problems, modified ghost fluid method, Hermite interpolation. AB -

In this paper, we develop a novel approach by combining a new robust finite difference Hermite weighted essentially non-oscillatory (HWENO) method [51] with the modified ghost fluid method (MGFM) [25] to simulate the compressible two-medium flow problems. The main idea is that we first use the technique of the MGFM to transform a two-medium flow problem to two single-medium cases by defining the ghost fluids status based on the predicted interface status. Then the efficient and robust HWENO finite difference method is applied for solving the single-medium flow cases. By using immediate neighbor information to deal with both the solution and its derivatives, the fifth order finite difference HWENO scheme adopted in this paper is more compact and has higher resolution than the classical fifth order finite difference WENO scheme of Jiang and Shu [14]. Furthermore, by combining the HWENO scheme with the MGFM to simulate the two-medium flow problems, less ghost point information is needed than that in using the classical WENO scheme in order to obtain the same numerical accuracy. Various one-dimensional and two-dimensional two-medium flow problems are solved to illustrate the good performances of the proposed method.

Zhuang Zhao, Yong-Tao Zhang, Yibing Chen & Jianxian Qiu. (2021). A Hermite WENO Method with Modified Ghost Fluid Method for Compressible Two-Medium Flow Problems. Communications in Computational Physics. 30 (3). 851-873. doi:10.4208/cicp.OA-2020-0184
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