A Subsonic-Well-Balanced Reconstruction Scheme for Shallow Water Flows
A Subsonic-Well-Balanced Reconstruction Scheme for Shallow Water Flows
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DOI：
10.1137/090758416
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发表时间：
2010-09
期刊：
影响因子：
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通讯作者：
F. Bouchut;T. M. D. Luna
中科院分区：
文献类型：
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作者：
F. Bouchut;T. M. D. Luna
本文考虑非平底浅水流动的圣维南方程组。在过去的几年中，已经提出了有效的平衡方法，以解决接近静态稳定状态的解决方案。在这里，我们描述了一个战略的基础上，当地的亚音速稳定状态重建，允许一个得到一个亚音速平衡良好的计划，保留正是所有的亚音速稳定状态。它概括了现在著名的流体静力学求解器，和后者一样，它保留了非负的水的高度，并满足半离散熵不等式。提出了一个应用到Euler-Poisson系统。
We consider the Saint-Venant system for shallow water flows with nonflat bottom. In past years, efficient well-balanced methods have been proposed in order to well resolve solutions close to steady states at rest. Here we describe a strategy based on a local subsonic steady state reconstruction that allows one to derive a subsonic-well-balanced scheme, preserving exactly all the subsonic steady states. It generalizes the now well-known hydrostatic solver, and like the latter it preserves the nonnegativity of the water height and satisfies a semidiscrete entropy inequality. An application to the Euler-Poisson system is proposed.