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The improved space–time conservation element and solution element scheme for two‐dimensional dam‐break flow simulation
Author(s) -
Zhang Yongxiang,
Zeng Zhong,
Chen Jingqiu
Publication year - 2011
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2525
Subject(s) - finite element method , robustness (evolution) , dam break , finite volume method , spacetime , grid , conservation law , mathematics , space (punctuation) , extended finite element method , space time , scheme (mathematics) , shallow water equations , flow (mathematics) , mathematical optimization , computer science , mathematical analysis , geometry , mechanics , engineering , physics , structural engineering , biochemistry , chemistry , philosophy , theology , quantum mechanics , chemical engineering , gene , operating system , flood myth
A new numerical scheme, namely space–time conservation element and solution element (CE/SE) method, has been used for the solution of the two‐dimensional (2D) dam‐break problem. Distinguishing from the well‐established traditional numerical methods (such as characteristics, finite difference, finite element, and finite‐volume methods), the CE/SE scheme has many non‐traditional features in both concept and methodology: space and time are treated in a unified way, which is the most important characteristic for the CE/SE method; the CEs and SEs are introduced, both local and global flux conservations in space and time rather than space only are enforced; an explicit scheme with a stagger grid is adopted. Furthermore, this scheme is robust and easy to implement. In this paper, an improved CE/SE scheme is extended to solve the 2D shallow water equations with the source terms, which usually plays a critical role in dam‐break flows. To demonstrate the accuracy, robustness and efficiency of the improved CE/SE method, both 1D and 2D dam‐break problems are simulated numerically, and the results are consistent with either the analytical solutions or experimental results. Copyright © 2011 John Wiley & Sons, Ltd.