An improved hydrostatic reconstruction method for shallow water model

Abstract

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.

Keywords:

• Finite volume method
• hydrostatic reconstruction
• shallow water equations
• uneven bed
• well-balanced scheme
• wetting and drying

Acknowledgments

China Scholarship Council and the Chair of Water Resources Management and Modeling of Hydrosystems in TU Berlin are gratefully acknowledged for the financial support for this work. The authors also appreciate Prof. Vladimir Nikora, the associate editor and the reviewers for the invaluable comments and suggestions, which play an important role to improve the quality of this paper.