Particle-laden flows on non-flat inclines in the settled regime: mathematical modeling and numerical investigations

Abstract Particle-laden flows on an inclined plane under the effect of gravity is considered. Through long-wave and dilute approximations of flows, effective in particular for dynamics with low inclination angle and particle concentrations, the model is simplified as a system of conservation or balance laws. The derivation of the evolution model including the effect of the non-flat bottoms towards the investigations of dynamics of particle-laden flows under various ambient constraints is the main issue in the present paper. It turns out that the inclusion of non-flat bottom effects is achieved as a natural extension of the flat-bottom setting in e.g., Murisic et al. (J Fluid Mech 717:203–231, 2013). Sample numerical simulations of flows on various inclined non-flat planes are also collected.