The overset grid technique has been illustrated with the use of several examples. These examples include droplet group dynamics, flow in porous media, and moving particles in pipes; the solutions have been accurate and efficient. The overset grid technique offers the advantages of high grid quality and a natural decomposition of multiple geometry problems onto parallel processors. For moving particles, the overset mesh technique seems to be particularly attractive since the need for remeshing is avoided. Copyright © 1999 John Wiley & Sons, Ltd.