Well-balanced hybrid compact-WENO scheme for shallow water equations

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• 作者：Qiangqiang Zhu^a ; ^{zqqouc2010@126.com} ; Zhen Gao^b ; ^{zhengao@ouc.edu.cn} ; Wai Sun Don^b ; ^{waisundon@gmail.com} ; Xianqing Lv^a ; ^{xqinglv@ouc.edu.cn}
• 关键词：Well-balanced ; WENO-Z ; Compact ; Multi-resolution ; Hybrid ; Shallow water equations
• 刊名：Applied Numerical Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：112
• 期：Complete
• 页码：65-78
• 全文大小：1466 K
• 卷排序：112

文摘

We investigate the performance of the high order well-balanced hybrid compact-weighted essentially non-oscillatory (WENO) finite difference scheme (Hybrid) for simulations of shallow water equations with source terms due to a non-flat bottom topography. The Hybrid scheme employs the nonlinear fifth order characteristic-wise WENO-Z finite difference scheme to capture high gradients and discontinuities in an essentially non-oscillatory manner, and the linear spectral-like sixth order compact finite difference scheme to resolve the fine scale structures in the smooth regions of the solution efficiently and accurately. The high order multi-resolution analysis is employed to identify the smoothness of the solution at each grid point. In this study, classical one- and two-dimensional simulations, including a long time two-dimensional dam-breaking problem with a non-flat bottom topography, are conducted to demonstrate the performance of the hybrid scheme in terms of the exact conservation property (C-property), good resolution and essentially non-oscillatory shock capturing of the smooth and discontinuous solutions respectively, and up to 2–3 times speedup factor over the well-balanced WENO-Z scheme.