Continuum mechanical modeling and higher-order accurate simulation of debris flows

泥石流是指泥沙颗粒和水的混合物沿着陡峭的斜坡向下重力驱动的水流。尽管在过去的几十年里，地球物理质量流的模拟和计算有了很大的发展，但这种固液多相流的预测仍然是最具挑战性的课题之一，主要体现在两个方面：(1)理论模拟和(2)高阶数值法。一方面，在大多数连续介质模型中，泥石流通常被视为单相介质，尽管泥石流显然是混合物。在这种单相方法中，碎屑混合物要么被视为包含某些塑性行为的非牛顿流体，要么被视为库仑连续体，其中孔隙流体所起的作用可以参数地结合在一起，或者被视为具有相同组成速度的混合物。构建泥石流多组分模型并将其应用于泥石流的研究非常罕见。现有的几个属于这种方法的模型包括各种弱点。它们的热力学一致性通常要么得不到验证，要么得不到满足。另一方面，对于数值方法，通常采用经典的数值技术，其中离散化的精度不可避免地在局部极值处退化到一阶。对于高分辨率TVD(总变化减小)方案也是如此。在这个项目中，我们将试图通过利用熵原理来建立描述流动的颗粒-流体混合物的热力学一致性混合模型。我所自2008年以来一直在开发的高精度间断Galerkin软件库BOSS(Bound Support Spectral Solver)将扩展到多组分混合物问题，以数值模拟颗粒-流体混合物的流动。泥石流沿着倾斜的平面汇入水平跳动区，特别是遇到障碍物时，将进行调查。

A debris flow represents gravity-driven flow of a mixture of sediment particles and water down a steep slope. Despite the development in modeling and computing geophysical mass flows in the past decades, the prediction of such solid-fluid multiphase flows is still one of the most challenging topics mainly in two aspects (i) theoretical modeling and (ii) higher-order numerical methods. On the one hand, in most continuum models, the debris flows are often treated as a single-phase medium, even though a debris flow is clearly a mixture. In such single-phase approaches, the debris mixture is considered either as a non-Newtonian fluid including some plastic behavior or as a Coulomb continuum where the role played by the pore fluid can be incorporated parametrically or as a mixture with the same constituent velocities. Very rare multi-constituent models are constructed and applied to debris flows. A few existing models belonging to this approach include various weaknesses. Their thermodynamic consistency is usually either not verified or not satisfied. On the other hand, regarding numerical methods, often classical numerical techniques are employed in which the accuracy of a discretization inevitably degrades to the first order at local extreme. This is also the case for high-resolution TVD (total variation diminishing) schemes. With this project, we will attempt to develop a thermodynamically consistent mixture model describing flowing granular-fluid mixtures by means of the exploitation of the entropy principle. The highly accurate discontinuous Galerkin software library BoSSS (Bounded Support Spectral Solver), which is under development since 2008 in our institute, will be extended with regard to multi-constituent mixture problems, to numerically examine flows of granular-fluid mixtures. Debris flows down an inclined plane merging into a horizontal run-out zone, especially encountering obstacles will be investigated.