An improved hydrostatic reconstruction method for shallow water model

Due to the universality, high efficiency and robustness, the hydrostatic non-negative water depth reconstruction method (HNRM) is attractive in solving the shallow water equations. However, the HNRM may lead to numerical failures when simulating dynamic shallow flows over uneven beds with large vari...

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Bibliographic Details
Published in:Journal of hydraulic research 2014-05, Vol.52 (3), p.432-439
Main Authors: Hou, Jingming, Simons, Franz, Liang, Qiuhua, Hinkelmann, Reinhard
Format: Article
Language:English
Subjects:
Earth sciences
Earth, ocean, space
Exact sciences and technology
Finite volume method
Hydrology
Hydrology. Hydrogeology
hydrostatic reconstruction
shallow water equations
uneven bed
well-balanced scheme
wetting and drying
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Summary:Due to the universality, high efficiency and robustness, the hydrostatic non-negative water depth reconstruction method (HNRM) is attractive in solving the shallow water equations. However, the HNRM may lead to numerical failures when simulating dynamic shallow flows over uneven beds with large variations on coarse meshes. In order to mitigate this problem, an improved HNRM (IHNRM) is proposed in this work by introducing an energy head to better evaluate the slope source terms, which may be wrongly computed by the HNRM in such cases. Besides, the IHNRM is able to preserve the conservation property and the non-negative water depth as the HNRM. The good performance of the IHNRM is verified against three test cases involving thin flows and wetting and drying over uneven beds.
ISSN:0022-1686
1814-2079
DOI:10.1080/00221686.2013.858648