In the present work a continuous model for fluid-particle flow computation is presented; the effects of particles are taken into account in terms of an effective viscosity, whereas the dispersed phase equation closure is simply based on particles buoyancy. The proposed approach allows the study of sediment transport without the need of curvilinear co-ordinate systems and the related step-by-step regridding, to describe accurately the evolution of bed forms. In fact in the present model the bottom shape is described in terms of a density contour line, rather then a moving boundary of the fluid domain. Numerical properties of discrete schemes for convective transport were carefully investigated by suitable test cases. The model has been validated in comparison with a Lagrangian approach, in the simple case of settling particles in a Couette flow.
The transport of sediments in a flowing current is one of the most important and less understood problems even though it has a fundamental relevance in many practical applications; these range from erosion processes in coastal and fiver engineering up to separation of particles and dynamics of suspensions in the chemical industry. The interaction between fluid and particles is a very complicated phenomenon owing to the dynamical feedback between the two phases and even for simple configurations the relationship between the fluid velocity and the mass transport it not known with reasonable accuracy. Even Einstein fated to tread in the sediment transport since he is reputed to have told his son … Son, don't mess with that, it's far too complicated … [1]. These problems can be attacked from two different viewpoints: a Lagrangian (discrete) or a Eulerian (continuous) approach.
