In this paper, we construct and study an exactly well‐balanced positivity‐preserving nonstaggered central scheme for shallow water flows in open channels with irregular geometry and nonflat bottom topography. We introduce a novel discretization of the source term based on hydrostatic reconstruction to obtain the exactly well‐balanced property for the still water steady‐state solution even in the presence of wetting and drying transitions. The positivity‐preserving property of the cross‐sectional wet area is obtained by using a modified “draining" time‐step technique. The current scheme is also Riemann‐solver‐free. Several classical problems of open‐channel flows are used to test these properties. Numerical results confirm that the current scheme is robust, exactly well‐balanced and positivity‐preserving.

中文翻译：

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精确平衡的积极性，为明渠水流保持无交错的中央方案

在本文中，我们构建并研究了具有不规则几何形状和非平坦底部地形的明渠中浅水流动的精确平衡的正性保全非交错式中心方案。我们引入基于静水力重构的源项的新颖离散化，即使在存在湿润和干燥转变的情况下，也能获得静态水稳态溶液的精确平衡的特性。通过使用改进的“排水”时间步长技术获得横截面湿区的正性，目前的方案也没有使用黎曼解算器，使用一些经典的明渠流动问题来测试这些问题。数值结果证实了当前方案是可靠的，完全平衡的和积极的。