LATERAL DIFFUSION IN FINITE DIFFERENCE SCHEMES FOR AVALANCHE SIMULATION

摘要

Modelling and simulation of granular materials is an active research field with applications in many industry sectors. Topics of interest range from microscopic problems, such as grain segregation to macroscopic phenomena, such as avalanches. The BCRE model (from the authors' names, Bouchaud, Cates, Ravi Prakash and Edwards) is a model that describes the evolution of an avalanche as a thin layer of rolling material over a basis of static grains. The model uses a system of two partial differential equations to compute simulations of the avalanche process. Depending on the numerical scheme used to solve the equations, there are some phenomena appearing in real avalanches which are not properly reproduced in the simulation. In this paper we focus on the lateral expansion of an avalanche that slides down a slope. We analyse two different finite difference schemes that can be used to solve the equations and prove that only one of them can simulate some expansion processes observed in real avalanches. We perform several simulations to show the properties deduced from our analysis.