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Robust absorbing boundary conditions for shallow water flow models

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Abstract

This paper investigates the cause of the spurious waves generated at the domain boundaries and proposes robust absorbing conditions in 2D shallow water simulations. The spurious waves are caused by the missing information when imposing boundary conditions for subcritical flows over irregular topography adjacent to the boundaries. The resulting boundary disturbances are likely to affect the flow solution inside the domain. To prevent the generation of such boundary spurious waves, an approach is proposed by extending the computational domain in the normal direction by a small number of cells. The number of extended cells is properly determined through numerical experiments by taking into account the effects of wave height, water depth, boundary topographic features (i.e., bump height, bump slope and bump type) and grid resolution. Five extended cells are found to be adequate in eliminating the spurious waves and maintaining stable and accurate numerical solutions. The robustness of the proposed boundary treatment is tested and confirmed through applications to reproduce two field-scale tsunami events.

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Acknowledgments

The authors acknowledge the support from the Royal Society under the International Exchanges 2013 NSFC cost share scheme (IE131297). This work is also partly supported by the National Natural Science Foundation of China through research grant (No. 51379074) and the Chinese Government through the ‘Recruitment Program of Global Experts’. The authors also thank Professor Tomohiro Yasuda from Kyoto University for providing the data for the second benchmark test.

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Authors and Affiliations

  1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing, China

    Jingming Hou & Qiuhua Liang

  2. School of Civil Engineering & Geosciences, Newcastle University, Newcastle upon Tyne, NE1 7RU, UK

    Jingming Hou, Qiuhua Liang & Xilin Xia

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  1. Jingming Hou
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  2. Qiuhua Liang
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  3. Xilin Xia
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Correspondence to Qiuhua Liang.

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Hou, J., Liang, Q. & Xia, X. Robust absorbing boundary conditions for shallow water flow models. Environ Earth Sci 74, 7407–7422 (2015). https://doi.org/10.1007/s12665-015-4743-6

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  • DOI: https://doi.org/10.1007/s12665-015-4743-6

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