A 3D Two-Phase Numerical Model for Sediment Transport

We have developed a three dimensional numerical model based on the two-phase equations to study the bed-load transport Chauchat and Médale (2009). We have considered two formulations of the model based on a two fluid or a single mixed-fluid description. The governing equations are discretized by a finite element method and a penalisation method is introduced to cope with the incompressibility constraint whereas a regularisation technique is used to deal with the visco-plastic behaviour of the granular phase. The accuracy and efficiency of the numerical models have been compared with the analytical solution of Ouriemi et al. (2009a). It turns out that one must takes a smaller regularisation parameter (one order of magnitude) in the mixed-model than in the two-fluid one for a comparable accuracy. Using an Arc Length Continuation algorithm coupled with this model we have investigated the evolution of the solution in terms of the height of the flowing granular layer and the particle flux against the longitudinal pressure gradient. The results of these simulations are in good agreement with the analytical solution in the 2D case and three-dimensional computations have been carried out in a square and circular cross-section ducts showing that the effect of the geometry is non-trivial.