At the start of each time step the particles at each site collide according to the particular collision rules for the model being used - the collision stage. After the collision stage each particle travels in a straight line along one of the lattice links, unless it is a rest particle, until it arrives at the next link - the streaming stage. The particles arriving at their new sites then collide at the beginning of the next time step. Figure 3-7
Figure 3-7: The evolution of particles on a portion of a square lattice
from time t-1 to time t+1.
shows the evolution of particles colliding and streaming on a square lattice according to the HPP collision rules. Note that although the exclusion principle allows only one particle to travel along each link direction two particles travelling in opposite directions are allowed on the same link, these particles pass each other during the streaming stage without colliding. As well as considering the discrete space of the lattice sites time is also considered as being discrete. Each particle jumps from its position at time t-1 to its position at time t where it collides instantaneously before jumping to its new position at time t+1.