1D Mathematical modelling of debris flow

Debris flow is modelled using the equations governing the dynamics of a liq uid-solid mixture. An upwind finite volume scheme;is applied to solve the r esulting differential equations in one dimension. These equations have a st ructure similar to those of the monophasic water flow, differing from them by the presence of some terms characteristic of the bifasic nature of the m ixture, such as granular bed erosion velocity, sediment concentration bed s hear stress, etc. The model and the system of equations to be solved are pr esented with the description of the implementation of the upwind scheme for the resulting hyperbolic conservation system. The numerical method is firs t order in both space and time. The treatment of the, source terms is speci fied in detail and some comparison with laboratory experiments are presente d.