考虑粘性效应的浅层两相泥石流多层模型
Multilayer models for shallow two-phase debris flows with dilatancy effects
摘要：
本文提出了一个考虑双折射效应的浅层颗粒-流体混合物的多层模型。它可以被看作是Bouchut等人（2016）提出的深度平均模型的推广，该模型通过考虑两层模型（混合颗粒-流体层和上层流体层）来包括双折射效应，以允许它们之间的流体交换。在目前的工作中，混合物层的近似得到了改善，包括正常的变化的速度和浓度的两个阶段由于多层的方法。在这里提出的模型中，双折射效应特别引起与超孔隙流体压力相关的两个相的非静水压力。我们确定了两相浅层泥石流模型求解的主要数值难点之一：从非平衡条件开始时，超孔隙流体压力的强非线性行为和突变。我们提出了一个简化的方法来近似的超孔隙流体压力在简单的情况下，均匀流。我们的方法使得有可能引入两个或三个层的正常方向与合理的近似。计算了均匀颗粒流体流过斜面的解析解，并与所提出的模型进行了比较。在数值结果中，我们观察到，所提出的模型与两层描述的混合物准确地表示在实验室实验中的混合物的表面处测量的速度。在单层模型中，深度平均速度显然不能很好地代表这一点。我们的数值计算结果表明，显着的影响，特别是在计算的时间演变的超孔隙流体压力的参数参与的粘性定律。
英文摘要：
We present here a multilayer model for shallow grain-fluid mixtures with dilatancy effects. It can be seen as a generalization of the depth-averaged model presented in Bouchut et al. (2016), that includes dilatancy effects by considering a two-layer model, a mixture grain-fluid layer and an upper fluid layer, to allow the exchange of fluid between them. In the present work the approximation of the mixture layer is improved including normal variations of the velocities and concentrations of the two phases thanks to the multilayer approach. In the model presented here dilatancy effects induce in particular a non-hydrostatic pressure for both phases related to the excess pore fluid pressure. We identified here one of the main numerical difficulty of solving two-phase shallow debris flows models: the strongly non-linear behaviour and abrupt changes of the excess pore fluid pressure when starting from non-equilibrium conditions. We propose a simplified approach to approximate the excess pore fluid pressure in the simple case of uniform flows. Our method makes it possible to introduce two or three layers in the normal directions with a reasonable approximation. Analytical solutions for uniform grain-fluid flows over inclined planes, with and without side wall friction, are calculated and compared to the proposed model. In the numerical results, we observe that the proposed model with a two layer description of the mixture accurately represents the velocity measured at the surface of the mixture in the laboratory experiments. This is obviously poorly represented by the depth-averaged velocity in single-layer models. Our numerical results show a significant impact of the parameters involved in dilatancy law, in particular on the calculation of the time evolution of the excess pore fluid pressure.
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