非均匀封闭水管非定常混合流模型及平衡有限体积格式
A model for unsteady mixed flows in non uniform closed water pipes and a well-balanced finite volume scheme
摘要：
本文提出了一个新的单向模型的推导。本文提出了一个新的单向模型的推导。我们引入了一个局部参考系来考虑截面和斜率变化引起的局部扰动。然后进行渐近分析，以获得一个模型的自由表面流动和另一个加压流。通过使用一组共同的变量和一个合适的压力定律，通过过渡点耦合这些模型，我们得到一个简单的公式称为PFS模型接近浅水方程的源项。它考虑了通过过渡点的连续方式的截面变化和斜率变化。两种流动之间的过渡点被视为与压力梯度的不连续性相关联的自由边界。数值模拟是通过使用Roe有限体积格式，我们适应考虑对流矩阵中的几何源项。最后给出了一些数值试验。
英文摘要：
We present the derivation of a new unidirectional model for We present the derivation of a new unidirectional model for unsteady mixed flows in non uniform closed water pipes. We introduce a local reference frame to take into account the local perturbation caused by the changes of section and slope. Then an asymptotic analysis is performed to obtain a model for free surface flows and another one for pressurized flows. By coupling these models through the transition points by the use of a common set of variables and a suitable pressure law, we obtain a simple formulation called PFS-model close to the shallow water equations with source terms. It takes into account the changes of section and the slope variation in a continuous way through transition points. Transition point between the two types of flows is treated as a free boundary associated to a discontinuity of the gradient of pressure. The numerical simulation is performed by making use of a Roe-like finite volume scheme that we adapted to take into account geometrical source terms in the convection matrix. Finally some numerical tests are presented.
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