Computational and experimental studies of rapid free-surface granular flows around obstacles

The study of the rapid free-surface granular flows that are driven under gravitational acceleration has attracted much attention in recent years. This is not only because such flows occur in many industrial and natural examples, but also because their transport mechanisms can be observed through small-scale lab experiments, modeled with continuum theories, and simulated by computers. When granular particles rapidly propagate around obstacles, the resulting phenomena - shock waves, particle free regions or granular vacua, expansion fans and stagnation zones - are of particular theoretical and practical importance. In this paper we develop a computational method for a hydraulic-type avalanche model that is able to simulate such phenomena. It numerically solves the avalanche model over a structured grid by including the topography of the obstacles. Different finite-difference TVD methods based on the non-oscillatory central (NOC) scheme are tested in computation to compare the resolution of the shock waves when granular flows propagate against an oblique wedge. This is also involved in the choice of the limiters, but which are shown rather insensitive in such computations. A level set formulation is coupled into the governing equations to follow the evolution of the boundaries of the granular vacua. It is tested in a situation when granular particles flow around a circular cylinder, where bow shock waves, granular vacua, expansion fans and stationary zones are all captured in the computation. These results agree well and consistently with the laboratory experiment