封闭水管中非稳态压力流的动力学格式
A kinetic scheme for unsteady pressurised flows in closed water pipes
AI总结：
提出一种用于封闭水管中瞬态压力流计算的动力学数值格式，基于守恒双曲偏微分系统的动力学公式，并通过对均匀管道水锤问题的数值验证，与工业代码结果吻合良好。
摘要：
本文旨在提出一种用于封闭水管中瞬态压力流计算的动力学数值格式。首先，我们详细描述了作为守恒双曲偏微分方程组的数学模型，并回顾了如何获得相应的动力学公式。然后，我们构建了动力学格式，确保了对由地形引起的源项进行迎风处理，该处理方式类似于Perthame等人通过浅水方程在微观层面上的能量平衡所描述的方式。最后，在均匀管道的水锤情况下进行验证：我们将EDF-CIH（法国）使用的工业代码（通过特征线法求解Allievi方程，即管道压力流常用方程）提供的数值结果与动力学格式的结果进行比较。结果表明它们非常吻合。
英文摘要：
The aim of this paper is to present a kinetic numerical scheme for the computations of transient pressurised flows in closed water pipes. Firstly, we detail the mathematical model written as a conservative hyperbolic partial differentiel system of equations, and the we recall how to obtain the corresponding kinetic formulation. Then we build the kinetic scheme ensuring an upwinding of the source term due to the topography performed in a close manner described by Perthame et al. using an energetic balance at microscopic level for the Shallow Water equations. The validation is lastly performed in the case of a water hammer in a uniform pipe: we compare the numerical results provided by an industrial code used at EDF-CIH (France), which solves the Allievi equation (the commonly used equation for pressurised flows in pipes) by the method of characteristics, with those of the kinetic scheme. It appears that they are in a very good agreement.
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