The extended finite element method for rigid particles in Stokes flow

A new method for the simulation of particulate ows, based on the extended nite element method (X-FEM), is described. In this method, the particle surfaces need not conform to the nite element boundaries, so that moving particles can be simulated without remeshing. The near eld form of the uid ow about each particle is built into the nite element basis using a partition of unity enrichment, allowing the simple enforcement of boundary conditions and improved accuracy over other methods on a coarse mesh. We present a weak form of the equations of motion useful for the simulation of freely moving particles, and solve example problems for particles with prescribed and unknown velocities