The extended finite element method for rigid particles in Stokes flow

TLDR

The study introduces a new extended finite element method (X‑FEM) for simulating particulate flows. X‑FEM allows particle surfaces to be non‑conforming to the mesh, incorporates near‑field flow via partition‑of‑unity enrichment, and uses a weak form of the equations of motion to enable simulation of freely moving particles without remeshing. The method accurately simulates particles with both prescribed and unknown velocities, demonstrating its effectiveness on example problems. © 2001 John Wiley & Sons, Ltd.

Abstract

Abstract A new method for the simulation of particulate flows, based on the extended finite element method (X‐FEM), is described. In this method, the particle surfaces need not conform to the finite element boundaries, so that moving particles can be simulated without remeshing. The near field form of the fluid flow about each particle is built into the finite 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. Copyright © 2001 John Wiley & Sons, Ltd.