Lattice Gas Automaton - Hexagonal Grids

Hexagonal Grids

The hexagonal grid model was first introduced in 1986, in a paper by Uriel Frisch, Brosl Hasslacher and Yves Pomeau, and this has become known as the FHP model after its inventors. The model has six or seven velocities, depending on which variation is used. In any case, six of the velocities represent movement to each of the neighboring sites. In some models (called FHP-II and FHP-III), a seventh velocity representing particles "at rest" is introduced. The "at rest" particles do not propagate to neighboring sites, but they are capable of colliding with other particles. The FHP-III model allows all possible collisions that conserve density and momentum. Increasing the number of collisions raises the Reynolds number, so the FHP-II and FHP-III models can simulate less viscous flows than the six-speed FHP-I model.

The simple update rule of FHP model proceeds in two stages, chosen to conserve particle number and momentum. The first is collision handling. The collision rules in the FHP model are not deterministic, some input situations produce two possible outcomes, and when this happens, one of them is picked at random. Since random number generation is not possible through completely computational means, a pseudorandom process is usually chosen.

After the collision step a particle on a link is taken to be leaving the site. If a site has two particles approaching head-on, they scatter. A random choice is made between the two possible outgoing directions that conserve momentum.

The hexagonal grid does not suffer as large anisotropy troubles as those that plague the HPP square grid model, a fortunate fact that is not entirely obvious, and that prompted Frisch to remark that "the symmetry gods are benevolent".