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A Well-Balanced and Positivity-Preserving Numerical Model for Shallow Water Flows in Channels with Wet–Dry Fronts

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Abstract

In this paper, a novel well-balanced and positivity-preserving finite-volume method for the shallow water flows in open channels with non-uniform width and irregular bottom topography is developed. Special attentions are paid to guarantee the well-balanced property not only over the fully submerged domain, but also in those partially flooded and dry regions near the wet–dry interfaces. Such property is achieved via a new method involving local surface reconstruction and special discretization of the geometric source terms. The desired properties of the proposed numerical schemes are verified by a number of numerical experiments.

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  1. Numerical Environmental Prediction Section, Canadian Meteorological Centre, Environment and Climate Change Canada, Dorval, QC, H9P 1J3, Canada

    Xin Liu

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  1. Xin Liu
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Liu, X. A Well-Balanced and Positivity-Preserving Numerical Model for Shallow Water Flows in Channels with Wet–Dry Fronts. J Sci Comput 85, 60 (2020). https://doi.org/10.1007/s10915-020-01362-2

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  • DOI: https://doi.org/10.1007/s10915-020-01362-2

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