In this paper, a model is presented for modeling saturated granular-liquid free-surface flows, in which the volume-averaged mixture bulk velocity is employed to derive the balance equations for the mass and momentum of mixture flow. Additionally, an evolution equation of the slip velocity between granular-and liquid constituents is derived to describe the separation between these constituents. The frictional-collisional constitutive relation for granular-constituent is employed to determine the stress due to particles interaction. The governing equations for mixture flows are numerically solved by a finite difference two-step projection method. The volume of fluid (VOF) method is employed to track the free surface of the mixture flow in the present numerical model. Good agreements between numerical results and experimental data are observed by modeling the dam-break process of granular-liquid mixture flow, dam-break waves over the saturated erodible beds and surge waves induced by submarine landslides along an inclined plane. Furthermore, the difference between the volume-averaged mixture bulk velocity and mass-averaged mixture bulk velocity is found to vary as the instinct density ratio of granular-constituent and liquid-constituent and the volumetric concentration n_s of the granular-constituent, and the evolution in the slip velocity during the process of the settlement of sediments is numerically analyzed.

中文翻译：

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饱和颗粒液体自由表面流的滑移速度混合模型

本文提出了一种模拟饱和颗粒液体自由表面流的模型，其中采用体积平均混合物体积速度来推导混合物流的质量和动量的平衡方程。此外，还导出了颗粒和液体成分之间滑移速度的演化方程来描述这些成分之间的分离。采用颗粒成分的摩擦碰撞本构关系来确定颗粒相互作用产生的应力。混合流控制方程采用有限差分两步投影法进行数值求解。在本数值模型中，采用流体体积（VOF）方法来跟踪混合物流动的自由表面。通过模拟颗粒-液体混合物流的溃坝过程、饱和侵蚀层上的溃坝波以及海底滑坡沿斜面引起的涌浪，数值结果与实验数据之间具有良好的一致性。此外，发现体积平均混合物堆积速度和质量平均混合物堆积速度之间的差异随着颗粒成分和液体成分的本能密度比以及颗粒成分的体积浓度ns_而变化，并且对沉积物沉降过程中滑移速度的演变进行了数值分析。