A space-time framework is applied to simulate dense granular flow. Two different numerical experiments are performed: a column collapse and a dam break on an inclined plane. The experiments are modeled as two-phase flows. The dense granular material is represented by a constitutive model, the $\mu$($I$)-rheology, that is based on the Coulomb's friction law, such that the normal stress applied by the pressure is related to the tangential stress. The model represents a complex shear thinning viscoplastic material behavior. The interface between the dense granular material and the surrounding light fluid is captured with a level set function. Due to discontinuities close to the the interface, the mesh requires a sufficient resolution. The space-time approach allows unstructured meshes in time and, therefore a well refined mesh in the temporal direction around the interface. In this study, results and performance of a flat and a simplex space time discretization are verified and analyzed.

中文翻译：

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在时空框架内使用$μ$（$ I $）流变学模拟密集的颗粒流

应用时空框架来模拟密集的颗粒流。进行了两个不同的数值实验：柱倒塌和斜面上的坝折断。实验被建模为两相流。致密的粒状材料由本构模型表示，即\\ mu $（$ I $）流变学，该模型基于库仑摩擦定律，因此，由压力施加的法向应力与切向应力有关。该模型代表了复杂的剪切稀化粘塑性材料的行为。致密的粒状材料与周围的轻质流体之间的界面通过水平设置功能捕获。由于靠近界面的不连续性，因此网格需要足够的分辨率。时空方法允许及时使用非结构化网格，并且 因此，在围绕界面的时间方向上，网格的精细度很高。在这项研究中，对平面和单纯形时空离散化的结果和性能进行了验证和分析。