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

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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.