顆粒流因為和山崩、土石流等環境流體具有部分相似的性質，故可藉由研究顆粒流的運動行為來推估山崩、土石流的特性，用以預測影響範圍及危害程度以達防災之目的，除了實驗方法外，近年來數值模擬也正蓬勃發展。本文的研究係將顆粒流分為流動層與底床層兩個部分，兩層之間透過侵蝕與堆積轉換，並考慮到山崩、土石流發生時底床的侵蝕堆積現象劇烈，底床傾角變動很大，亦即地形曲率的變化很大。目前有將地形曲率以離心力的形式考慮進控制方程式中，但對於其他可能受曲率影響的流體參數之研究尚缺乏，因此本研究著重於曲率在動態地形上對流體行為之影響，包含流體厚度、運移距離、侵蝕/堆積率和網格大小等。並透過地形座標系統將理論模型建立在隨變動底床運動的座標軸上，以此來描述顆粒流在可侵蝕底床上的動態行為。數值方法使用兼具shock-capturing特性的Non-Oscillatory Central (NOC) scheme，探討流體行為在不同曲率變化上的影響。

In order to predict the propagation, path and run-out distance of landslides and debris flows, it is of special interest to research the property of granular flows. In the present study, there is a non-material singular surface with mass flux through it which divides granular flows into two layers: a rapid surface flowing layer and a stagnant base. When landslides or debris flows occur, the erosion and deposition proceed between the two layers. The model equations are derived either in conventional Cartesian coordinates system with topographic correction or in curve-linear coordinate system with shallow curvature. Up to now, the contribution of the local curvature in the model equations is the centrifugal force alone. The study of the other effects caused by curvature on the flow behavior is rather rare. In this paper, we focus on how the local curvature influence the flow behavior, such as the flow thickness, run-out distance, erosion/deposition rate or even the mesh-size-dependency. The evolution of the topography is described by a moving coordinate model. For the numerical method, we use a shock-capturing non-oscillatory central (NOC) scheme. The numerical results show that our theory is a remarkably qualitative agreement between the simulation and the one-sided collapse flow experiment.

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