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High Order Well-Balanced Weighted Compact Nonlinear Schemes for Shallow Water Equations
Gao, Zhen1; Hu, Guanghui2,3

In this study, a numerical framework of the high order well-balanced weighted compact nonlinear (WCN) schemes is proposed for the shallow water equations based on the work in [S. Zhang, S. Jiang, C.-W Shu, J. Comput. Phys. 227 (2008) 7294-7321]. We employ a special splitting technique for the source term proposed in [Y. Xing, C.-W Shu, J. Comput. Phys. 208 (2005) 206-227] to maintain the exact C-property, which can be proved theoretically. In the meantime, the genuine high order accuracy of the numerical scheme can be observed successfully, and small perturbation of the stationary state can be resolved and evolved well. 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 scheme are used to construct different WCN schemes. In addition, the local characteristic projections are considered to further restrain the potential numerical oscillations. A variety of representative one-and two-dimensional examples are tested to demonstrate the good performance of the proposed schemes.

KeywordShallow Water Equations C-property Weighted Compact Nonlinear Scheme Source Term
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Indexed BySCIE
WOS Research AreaPhysics
WOS SubjectPhysics, Mathematical
WOS IDWOS:000405928100008
The Source to ArticleWOS
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Cited Times [WOS]:4   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
Affiliation1.Ocean Univ China, Sch Math Sci, Qingdao, Peoples R China
2.Univ Macau, Dept Math, Macau, Peoples R China
3.UM Zhuhai Res Inst, Zhuhai, Guangdong, Peoples R China
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GB/T 7714
Gao, Zhen,Hu, Guanghui. High Order Well-Balanced Weighted Compact Nonlinear Schemes for Shallow Water Equations[J]. COMMUNICATIONS IN COMPUTATIONAL PHYSICS,2017,22(4):1049-1068.
APA Gao, Zhen,&Hu, Guanghui.(2017).High Order Well-Balanced Weighted Compact Nonlinear Schemes for Shallow Water Equations.COMMUNICATIONS IN COMPUTATIONAL PHYSICS,22(4),1049-1068.
MLA Gao, Zhen,et al."High Order Well-Balanced Weighted Compact Nonlinear Schemes for Shallow Water Equations".COMMUNICATIONS IN COMPUTATIONAL PHYSICS 22.4(2017):1049-1068.
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