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A well-balanced spectral volume scheme with the wetting–drying property for the shallow-water equations

机译：具有浅水方程的干湿特性的平衡谱体积方案

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摘要

The shallow-water equations are widely used to model surface water bodies, such as lakes, rivers and the swash zone in coastal flows. Physically congruent solutions are characterized by nonnegative water depth, and many numerical methods may fail to preserve this property at the discrete level when moving wet–dry transitions are present in the physical domain. In this paper, we present a spectral-volume method for the approximate solution of the one-dimensional shallow-water\udequations, which is third-order accurate in wet regions, far from discontinuities, and which is well balanced for water at rest states: the stability of the solution is ensured if reconstruction and\udlimitation of variables preserves non-negativity of the depth and a suitable constraint for the time\udstep length is satisfied. A number of numerical experiments are reported, showing the promising\udcapabilities of the model to solve problems with non-trivial topographies and friction.
机译：浅水方程被广泛用于模拟地表水体，例如沿海水流中的湖泊，河流和冲积带。物理上一致的解决方案的特征是非负水深，当物理域中出现干湿转换时，许多数值方法可能无法在离散级别上保留此特性。本文针对一维浅水\渗流的近似解提出了一种频谱量法，该方法在湿润区域是三阶精确的，没有不连续性，并且对于静止状态下的水具有很好的平衡：如果变量的重建和限制保留了深度的非负性并且满足了对时间长度的适当约束，则可以确保解决方案的稳定性。报告了许多数值实验，显示了该模型解决非平凡地形和摩擦问题的有前途的能力。

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