We present a grain-fluid mixture for debris flows moving on a rugged (non-trivial) topography, where entrainment and deposition may take place. The model equations are derived with respect to a terrain-following coordinate system, which is constructed based on the topographic surface. The coordinates are fixed in space, and a “sub-topography” is added on the coordinate surface to account for the variation in the local topography when entrainment or deposition takes place. Numerical implementation is made based on a GPU-accelerated simulation tool, into which the entrainment-deposition mechanism is integrated accordingly. Two numerical examples are assigned to investigate the key features of the proposed model. One is on a horizontal plane, on which a finite mass of grain-fluid mixture is released from the state of rest. In this example, debris flow deposits significantly impact the post-event morphology and the associated flow behaviors. The other concerns a moving mass down an inclined chute merging into a horizontal deposition plane, where the levee formation is reproduced. At the end, the model is validated against grain-water experiments and applied to a large-scale historical event to evaluate its applicability.

中文翻译：

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用两相方法模拟崎岖地形上沉积和夹带的颗粒流体流动


我们提出了一种颗粒-流体混合物，用于在崎岖（非平凡）地形上移动的泥石流，其中可能发生夹带和沉积。模型方程是根据地形跟随坐标系推导的，该坐标系是基于地形表面构建的。坐标在空间中是固定的，并在坐标表面上添加“子地形”，以解释发生夹带或沉积时局部地形的变化。数值实现是基于GPU加速模拟工具进行的，相应地集成了夹带沉积机制。分配了两个数值示例来研究所提出模型的关键特征。一个是在水平面上，在该平面上，有限质量的颗粒-液体混合物从静止状态释放出来。在此示例中，泥石流沉积物显着影响事件后形态和相关的流动行为。另一个涉及沿着倾斜溜槽向下移动的质量，合并到水平沉积平面中，在该平面上再现了堤坝的形成。最后，该模型通过粮水实验进行验证，并应用于大规模历史事件以评估其适用性。