Discrete element method (DEM) has been used over the past 25 years for modelling many applications, starting with small systems in simple geometries in two dimensions, such as periodic cells and chute flows, small hoppers and shear cells (Campbell, 1990; Cundall and Strack, 1979; Haff and Werner, 1986; Walton, 1994). This leads to early industrial applications that can be characterised by small scales (100-1,000s of particles) with idealised assumptions and generally in two dimensions. Examples include ball mills (Mishra and Rajamani, 1992, 1994) and hoppers by numerous authors. Similarly, geophysical modelling using DEM started with small scales and idealised particles (Cleary and Campbell, 1993; Hopkins et al., 1991).

Through the 1990s, the problem sizes tackled increased in the range 10,000-100,000, but models were generally either two-dimensional (Campbell et al., 1995; Cleary, 1998a; Holst et al., 1999; P schel and Buchholtz, 1995; Potapov and Campbell, 1996a; Ristow, 1994; Thornton et al., 1996 and many others) or three-dimensional, but with very simple geometries (Cleary and Sawley, 1999; Potapov and Campbell, 1996b and many others).

DEM has currently progressed to the point where large scale industrial and geophysical systems can be modelled with increasing realism. Large scale DEM applications (as of 2003, since the threshold is time varying) can be characterised as having most or all of the following attributes.

• Models with at least 100,000 particles and up to in excess of 1 million particles.

• Very complex boundary geometries (sometimes executing complex motion) typically described using surface meshes...