Physical mechanisms at the origin of the transport of solid particles in a fluid are still a matter of debate in the physics community. Yet, it is well known that these processes play a fundamental role in many natural configurations, such submarines landslides and avalanches, which may have a significant environmental and economic impact. The goal here is to reproduce the local dynamics of such systems from the grain scale to that of thousands of grains approximately. To this end a simple soft-sphere collision / immersed-boundary method has been developed in order to accurately reproduce the dynamics of a dense granular media collapsing in a viscous fluid. The fluid solver is a finite-volume method solving the three-dimensional, time-dependent Navier-Stokes equations for a incompressible flow on a staggered. Here we use a simple immersed-boundary method consisting of a direct forcing without using any Lagrangian marking of the boundary, the immersed boundary being defined by the variation of a solid volume fraction from zero to one. The granular media is modeled with a discrete element method (DEM) based on a multi-contact soft-sphere approach. In this method, an overlap is allowed between spheres which mimics the elasto-plastic deformation of real grain, and is used to calculate the contact forces based on a linear spring model and a Coulomb criterion. Binary wall-particle collisions in a fluid are simulated for a wide range of Stokes number ranging from 10-¹ to 10⁴. It is shown that good agreement is observed with available experimental results for the whole range of investigated parameters, provided that a local lubrication model is used when the distance of the gap between the particles is below a fraction of the particle radius. A new model predicting the coefficient of restitution as a function of the Stokes number and the relative surface roughness of the particles is proposed. This model, which makes use of no adjustable constant, is shown to be in good agreement with available experimental data. Finally, simulations of dense granular flows in a viscous fluid are performed. The present results are encouraging and open the way for a parametric study in the parameter space initial aspect ratio - initial packing.
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