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首页> 外文期刊>Journal of Computational Physics >Efficient well-balanced hydrostatic upwind schemes for shallow-water equations
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Efficient well-balanced hydrostatic upwind schemes for shallow-water equations

机译：浅水方程组的高效平衡良好的静水迎风方案

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The proposed work concerns the numerical approximations of the shallow-water equations with varying topography. The main objective is to introduce an easy and systematic technique to enforce the well-balance property and to make the scheme able to deal with dry areas. To access such an issue, the derived numerical method is obtained by involving the free surface instead of the water height and this produces the scheme well-balanced independently from the numerical flux function associated with the homogeneous problem. As a consequence, we obtain an easy well-balanced scheme which preserves non-negative water height. When compared with the well-known hydrostatic reconstruction, the presented topography discretization does not involve any max function known to introduce some numerical errors as soon as the topography admits very strong variations or discontinuities. A second-order MUSCL accurate reconstruction is adopted. The proposed hydrostatic upwind scheme is next extended for considering 2D simulations performed over unstructured meshes. Several 1D and 2D numerical experiments are performed to exhibit the relevance of the scheme.
机译：拟议的工作涉及具有变化地形的浅水方程的数值近似。主要目的是引入一种简单而系统的技术来增强平衡性能，并使该方案能够处理干旱地区。为了解决这个问题，通过涉及自由表面而不是水高度来获得导出的数值方法，并且这产生了与均质问题相关的数值通量函数无关的良好平衡的方案。结果，我们获得了一个容易保持良好平衡的方案，该方案可以保持非负水位。与众所周知的静水压力重建相比，只要地形允许非常强的变化或不连续性，所提出的地形离散化就不会涉及任何已知的引入某些数值误差的最大函数。采用二阶MUSCL精确重建。接下来，将对拟议的静水迎风方案进行扩展，以考虑在非结构化网格上执行的2D模拟。进行了几次一维和二维数值实验，以显示该方案的相关性。

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