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.

中文翻译：

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干湿锋面河道中浅水流动的平衡性和正性数值模型

本文针对宽度不均，底部地形不规则的明渠浅水流问题，提出了一种平衡性好，保正性的新方法。要特别注意，以确保不仅在完全淹没的区域内，而且在湿-干界面附近的部分淹水和干旱地区，都具有良好的平衡特性。通过涉及局部表面重建和几何源项的特殊离散化的新方法来实现这种特性。通过许多数值实验验证了所提出数值方案的期望特性。