Granular matter (sand, rocks, gravels...) flows like a viscous fluid, but also resists shear stress like a solid. It evolves from one state to the other over a typical distance of a few grain diameters. Here we adopt the fluid point of view and discribe granular matter as a continuum with the so called µ(I) rheology: a plastic rheology where the normal and shear stress are proportional (Coulomb friction law).
This non-Newtonian rheology is implemented in a 2D Navier-Stokes solver (Gerris). Moreover, comparison with Contact Dynamics simulations (the displacement of all the grains is computed) with Shallow-Water models and experiments show the reliability of the μ(I)-rheology when modeling complex flow of granular matter in cases of avalanche flows (Bagnold flow), collapse of columns and flow in hourglass.
Flow in a sand glass
Discrete Contact Dynamics Continuum Flow