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

泥石流是由重力驱动的泥沙颗粒和水的混合物沿陡坡流下的水流。尽管地球物理质量流的模拟和计算在过去几十年有了发展，但这种固-流多相流的预测仍然是最具挑战性的课题之一，主要集中在两个方面(1)理论建模和(2)高阶数值方法。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，尽管泥石流显然是一种混合物。在这种单相方法中，碎屑混合物要么被视为具有某些塑性行为的非牛顿流体，要么被视为库仑连续体，其中孔隙流体的作用可以被参数化，要么被视为具有相同组成速度的混合物。建立并应用于泥石流的多组分模型是非常罕见的。属于这种方法的一些现有模型包含各种弱点。它们的热力学一致性通常要么没有得到验证，要么不满足。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下降到一阶。高分辨率TVD（总变差递减）方案也是如此。在这个项目中，我们将尝试开发一个热力学一致的混合模型，通过利用熵原理来描述流动的颗粒-流体混合物。高精度的不连续Galerkin软件库BoSSS （Bounded Support Spectral Solver）自2008年以来一直在我们研究所开发，将扩展到多组分混合物问题，以数值研究颗粒-流体混合物的流动。将研究沿斜面向下汇入水平跑出区的泥石流，特别是遇到障碍物的泥石流。

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.