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首页> 外文期刊>Journal of Computational Physics >Wave Riemann description of friction terms in unsteady shallow flows: Application to water and mud/debris floods
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Wave Riemann description of friction terms in unsteady shallow flows: Application to water and mud/debris floods

机译：Wave Riemann描述非稳态浅水流动中的摩擦项：在水和泥浆/碎石洪水中的应用

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摘要

In this work, the source term discretization in hyperbolic conservation laws with source terms is considered using an approximate augmented Riemann solver. The technique is applied to the shallow water equations with bed slope and friction terms with the focus on the friction discretization. The augmented Roe approximate Riemann solver provides a family of weak solutions for the shallow water equations, that are the basis of the upwind treatment of the source term. This has proved successful to explain and to avoid the appearance of instabilities and negative values of the thickness of the water layer in cases of variable bottom topography. Here, this strategy is extended to capture the peculiarities that may arise when defining more ambitious scenarios, that may include relevant stresses in cases of mud/debris flow. The conclusions of this analysis lead to the definition of an accurate and robust first order finite volume scheme, able to handle correctly transient problems considering frictional stresses in both clean water and debris flow, including in this last case a correct modelling of stopping conditions.
机译：在这项工作中，使用近似增强的黎曼求解器来考虑双曲线守恒律中带有源项的源项离散化。将该技术应用于具有床坡度和摩擦项的浅水方程，重点是摩擦离散化。增强的Roe近似Riemann解算器为浅水方程提供了一系列弱解，这是源项迎风处理的基础。事实证明，这种方法可以成功地解释和避免在底部地形变化的情况下出现水层厚度的不稳定性和负值。在这里，此策略已扩展为捕获在定义更宏大的方案时可能出现的特性，其中可能包括泥浆/泥石流情况下的相关应力。该分析的结论导致了一个准确而健壮的一阶有限体积方案的定义，该方案能够考虑到净水和泥石流中的摩擦应力，能够正确处理瞬态问题，包括在最后一种情况下的正确的停车条件建模。

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