Particulate flow simulations using lubrication theory solution enrichment

A technique for the numerical simulation of suspensions of particles in uid based on the extended nite element method (X-FEM) is developed. In this method, the particle surfaces need not conform to the nite element boundaries, so that moving particles can be simulated without remeshing. The nite element basis is enriched with the Stokes ow solution for ow past a single particle and the lubrication theory solution for ow between particles. The latter enrichment allows the simulation of particles that come arbitrarily close together without re ning the mesh in the gap between them. Example problems illustrating both types of enrichment are shown, along with a study of a 50% solution in channel ow.