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首页> 外文期刊>Journal of Computational Physics >Well-balanced and energy stable schemes for the shallow water equations with discontinuous topography
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Well-balanced and energy stable schemes for the shallow water equations with discontinuous topography

机译：地形不连续的浅水方程组的均衡和能量稳定方案

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摘要

We consider the shallow water equations with non-flat bottom topography. The smooth solutions of these equations are energy conservative, whereas weak solutions are energy stable. The equations possess interesting steady states of lake at rest as well as moving equilibrium states. We design energy conservative finite volume schemes which preserve (i) the lake at rest steady state in both one and two space dimensions, and (ii) one-dimensional moving equilibrium states. Suitable energy stable numerical diffusion operators, based on energy and equilibrium variables, are designed to preserve these two types of steady states. Several numerical experiments illustrating the robustness of the energy preserving and energy stable well-balanced schemes are presented.
机译：我们考虑具有非平坦底部地形的浅水方程。这些方程的光滑解是能量守恒的，而弱解是能量稳定的。这些方程式具有静止的湖泊有趣的稳态以及运动的平衡态。我们设计了能量保守的有限体积方案，该方案保留了（i）一维和二维空间中处于静止状态的湖泊，以及（ii）一维移动平衡态。基于能量和平衡变量的合适的能量稳定数值扩散算子被设计为保留这两种类型的稳态。提出了几个数值实验，说明了节能和能量稳定均衡方案的鲁棒性。

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