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High Order Well-Balanced Weighted Compact Nonlinear Schemes for the Gas Dynamic Equations under Gravitational Fields
Gao,Zhen1; Hu,Guanghui2,3
2017
Source PublicationEast Asian Journal on Applied Mathematics
ISSN2079-7362
Volume7Issue:4Pages:697-713
AbstractIn this study, we propose a high order well-balanced weighted compact nonlinear (WCN) scheme for the gas dynamic equations under gravitational fields. The proposed scheme is an extension of the high order WCN schemes developed in (S. Zhang, S. Jiang, C.-W Shu, J. Comput. Phys. 227 (2008) 7294-7321). For the purpose of maintaining the exact steady state solution, the well-balanced technique in (Y. Xing, C.-W Shu, J. Sci. Comput. 54 (2013) 645-662) is employed to split the source term into two terms. The proposed scheme can maintain the isothermal equilibrium solution exactly, genuine high order accuracy and resolve small perturbations of the hydrostatic balance state on the coarse meshes. Furthermore, in order to capture the strong discontinuities and large gradients, the fifth-order upwind weighted nonlinear interpolations together with the fourth/sixth order cell-centered compact schemes with local characteristic projections are used to construct different WCN schemes. Several representative one- and two-dimensional examples are simulated to demonstrate the good performance of the proposed schemes.
KeywordEuler equations gravitational fields source term steady state solution weighted compact nonlinear Scheme
DOI10.4208/eajam.181016.300517g
URLView the original
Language英语
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Document TypeJournal article
CollectionUniversity of Macau
Corresponding AuthorHu,Guanghui
Affiliation1.School of Mathematical Sciences,Ocean University of China,Qingdao,China
2.Department of Mathematics,University of Macau,Macao
3.UM Zhuhai Research Institute,Zhuhai, Guangdong Province,China
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Gao,Zhen,Hu,Guanghui. High Order Well-Balanced Weighted Compact Nonlinear Schemes for the Gas Dynamic Equations under Gravitational Fields[J]. East Asian Journal on Applied Mathematics,2017,7(4):697-713.
APA Gao,Zhen,&Hu,Guanghui.(2017).High Order Well-Balanced Weighted Compact Nonlinear Schemes for the Gas Dynamic Equations under Gravitational Fields.East Asian Journal on Applied Mathematics,7(4),697-713.
MLA Gao,Zhen,et al."High Order Well-Balanced Weighted Compact Nonlinear Schemes for the Gas Dynamic Equations under Gravitational Fields".East Asian Journal on Applied Mathematics 7.4(2017):697-713.
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