Numerical modeling of avalanches based on Saint-Venant equations using a kinetic scheme
Numerical modeling of avalanches based on Saint-Venant equations using a kinetic scheme
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DOI：
10.1029/2002jb002024
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发表时间：
2003-11
影响因子：
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通讯作者：
A. Mangeney-Castelnau;J. Villotte;M. Bristeau;Benoît;Perthame;F. Bouchut;C. Simeoni;S. Yerneni-S.-Yernen
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文献类型：
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作者：
A. Mangeney-Castelnau;J. Villotte;M. Bristeau;Benoît;Perthame;F. Bouchut;C. Simeoni;S. Yerneni-S.-Yernen
[1]本文提出了泥石流崩塌的数值模拟方法。该模型使用长波近似的基础上的小纵横比的碎片雪崩在经典的圣维南模型的浅水。使用这种近似的深度平均方程推导出一个参考帧链接到地形。泥石流在这里被视为一个单相，干颗粒流库仑型行为。数值有限体积法使用基于系统微观行为描述的动力学方案来定义有限元网格界面处的数值通量。该方法的主要优点是保持高度正性。该方案的独创性在于引入了微观尺度上粒子的狄拉克分布，以描述当驱动力低于库仑阈值时颗粒物质的停止。溃坝问题的解析解和实验结果的比较表明，该模型在处理显着的不连续性和再现流动和停止阶段的颗粒雪崩的效率。该模型描述碎片雪崩行为的能力在这里说明了简化的地形雪崩的示意性数值模拟。在这个简单的例子的框架中，比较了具有恒定摩擦角和可变摩擦角的库仑型行为。数值试验表明，这样的方法不仅提供了洞察流动和停止阶段的颗粒物质，但允许观察有趣的行为，如在特定情况下，停止固体状颗粒物质后面的流体状区域的存在，这表明在沉积质量的水平表面的存在。
[1] Numerical modeling of debris avalanche is presented here. The model uses the long-wave approximation based on the small aspect ratio of debris avalanches as in classical Saint Venant model of shallow water. Depth-averaged equations using this approximation are derived in a reference frame linked to the topography. Debris avalanche is treated here as a single-phase, dry granular flow with Coulomb-type behavior. The numerical finite volume method uses a kinetic scheme based on the description of the microscopic behavior of the system to define numerical fluxes at the interfaces of a finite element mesh. The main advantage of this method is to preserve the height positivity. The originality of the presented scheme stands in the introduction of a Dirac distribution of particles at the microscopic scale in order to describe the stopping of a granular mass when the driving forces are under the Coulomb threshold. Comparisons with analytical solutions for dam break problems and experimental results show the efficiency of the model in dealing with significant discontinuities and reproducing the flowing and stopping phase of granular avalanches. The ability of the model to describe debris avalanche behavior is illustrated here by schematic numerical simulation of an avalanche over simplified topography. Coulomb-type behavior with constant and variable friction angle is compared in the framework of this simple example. Numerical tests show that such an approach not only provides insights into the flowing and stopping stage of the granular mass but allows observation of interesting behavior such as the existence of a fluid-like zone behind a stopped solid-like granular mass in specific situations, suggesting the presence of horizontal surfaces in the deposited mass.