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High Order Well-Balanced Weighted Compact Nonlinear Schemes for Shallow Water Equations

Part of: Hyperbolic equations and systems

Published online by Cambridge University Press:  28 July 2017

Zhen Gao  and
Guanghui Hu
Zhen Gao*
Affiliation:
School of Mathematical Sciences, Ocean University of China, Qingdao, China
Guanghui Hu*
Affiliation:
Department of Mathematics, University of Macau, Macao SAR, China UM Zhuhai Research Institute, Zhuhai, Guangdong, China
*
*Corresponding author. Email addresses:zhengao@ouc.edu.cn (Z. Gao), garyhu@umac.mo (G. H. Hu)
*Corresponding author. Email addresses:zhengao@ouc.edu.cn (Z. Gao), garyhu@umac.mo (G. H. Hu)
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Abstract

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.

Keywords

Shallow water equationsC-propertyweighted compact nonlinear schemesource term

MSC classification

Secondary: 35L65: Conservation laws 35L67: Shocks and singularities
Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 4 , October 2017 , pp. 1049 - 1068
Copyright
Copyright © Global-Science Press 2017 

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