Porous Effects in the Description of the Dynamics of Granular Avalanches

Abstract

Granular mixtures are porous media of immense importance in geophysical and industrial applications. Snow avalanches, debris- and mud-flows, landslides and rockslides are examples of rapid flows of geomaterials whereas flows of fine granular materials in silos, hoppers, rotating drums and heap formations are examples from process engineering. In order to understand these phenomena properly, one needs physical-mathematical descriptions including appropriate constitutive relations and suitable numerical simulations. We present recently developed model equations by Pudasaini & Hutter for free gravity-driven flows of a single phase dry granular material down complicated real mountain terrains generated by arbitrary space curves with slowly varying curvature and torsion. These are very important extensions to the successful Savage-Hutter (SH) theory. Because of the density preserving assumption the effect of the porosity can only be accounted for in the closure statements. This is done here and its consequences are illustrated. Shock-capturing numerical schemes are used to integrate the model hyperbolic conservation system of equations in order to control spurious jumps in the mapping of the descending masses. The physical significance of the numerical simulations is discussed.