A many-body lubrication model

In [2], we presented direct numerical simulations of the motion of solid particles in a viscous fluid. In such simulations, numerical problems are likely to occur when particles get very close to each other: the mesh is to be refined in the gap zone, which is computationally expensive. In order to overcome this problem, we introduce here a lubrication model to handle those ''near collisions''. The objective is to couple this new approach with the global computation of the flow. Nevertheless, we will concentrate in the present paper on the lubrication model only. Indeed, the physical situation we will be dealing with is the motion of a close-packed arrangement of particles in a fluid, such that the influence of the fluid on the global behavior is restricted to lubrication forces.