Depth averaged modelling of loose rectangular granular piles collapsing in water

The collapse of a submerged granular pile under the action of the gravity force is investigated by means of a depth averaged model (hereinafter DAM). The granular pile is a mixture of solid particles and ambient liquid, totally covered by a layer of ambient liquid. The DAM is obtained by depth-averaging the mass and momentum equations of the mixture and the ambient fluid and is aimed at providing estimates of technical quantities regarding the considered phenomenon. The DAM is numerically solved by adopting an equivalent Discrete Boltzmann Equation model (hereinafter DBE) as solution method. The main advantage yielded by the DBE is the possibility to turn the original system of strongly non linear partial differential equations, which would require the resort to complex numerical schemes, into a purely advective, linear, first order one. Previously published experimental and numerical data, relative to the collapse of loose rectangular granular piles in water, are reproduced by the proposed model and a satisfactory agreement is found, revealing that the DAM is able to describe reliably the overall dynamics, in terms of quantities of technical interest as the height of the submerged granular flow and the instantaneous position of its front.