Fluid–particle flow simulation by averaged continuous model

In this paper we present a numerical method for fluid–particle flow simulation. The mathematical model is based on the averaged continuum. The presence of particles is taken into account in terms of effective viscosity, which is defined by means of both Newtonian and non-Newtonian (Bingham plastic) models. The dispersed phase equation closure is based on particle buoyancy as well as on shear-induced self-diffusion effects. The proposed approach allows us to study sediment transport problems and the related evolution of bed forms, without requiring the generation of curvilinear coordinate systems and time-consuming step-by-step regridding. In fact, the present model describes the bottom shape in terms of a density contour surface, rather than a moving boundary of the fluid domain. Simple two-dimensional numerical tests have been performed: (i) Bingham flow in a driven cavity and (ii) particle settling in a pure Couette flow. Finally, preliminary results concerning (iii) two-dimensional scour below pipelines in steady flow have been presented and discussed.