Lattice gas automaton

FHP the model is a fundamental model lattice gas and a cellular automaton for the simulation of gases and liquids. It is also known as Lattice Gas Cellular Automata ( LGCA ) known.

History

The FHP model was set up in 1986 by Uriel Frisch, Hasslacher, and Yves Pomeau Brosl whose initials are eponymous for the model. With the HPP model by Hardy, Pomeau and de Pazzi in 1973, it has historically been a precursor. The reason for the relatively long period of 13 years until the development is that the HPP model lacked the isotropy as an important property and it was believed that such models could not in principle be isotropic. After the isotropy was demonstrated for the FHP model, quickly began an intensive study of the model and a number of variants. The discovery of isotropy in the FHP model in conjunction with the high computational efficiency led on the one hand, there are reported the FHP model on the front page of the Washington Post, on the other hand, there was previously thinking this and any research on it as secret and militarily significant to be classified, and consequently to suppress publications so.

Model

As the term lattice - gas states, the entire dynamic plays out on a grid. In the case of FHP model there is a grid of equilateral triangles louder. There consequently exists a sixfold (discrete ) rotational symmetry. The triangular lattice is the crucial difference to the HPP model, which is based on an orthogonal grid ( checkerboard ).

• Particles still exist only on the grid points, that is, never on the edge and never on the surfaces.
• Each particle has an associated direction (from a grid point to another immediately adjacent ).
• A grid point, for each direction at most one particle, ie total of between zero and six particles contain.
• The particles are about as advanced. Between the coatings will be reviewed, whether it is at a lattice point in a dispersion.

Scattering: For scattering occurs when the same are two, three or four particles on a lattice point whose pulses ( directions) add up to zero. For two particles, this means that the particles must have the opposite direction in three that the angle between the particles must be 120 ° and four particles that unoccupied directions must be opposite. In the scattering of two particles both directions are rotated by 60 ° to the right or to the left, the direction of the deflection is chosen randomly and with equal probability (50:50). Three in the scattering of particles occupied and unoccupied directions are changed, and in the scattering of particles, the four unoccupied direction is rotated by 60 ° to the right or left. In any case, the pulse total is therefore also in accordance with the dispersion zero. This is the entire model - apart from edge effects - the momentum conservation guaranteed. In a deterministic version of the model is not chosen at random on the deflection direction, but alternately deflected to the right and left. For the same initial conditions follows a simulation sequence is always the same in this case.

Properties

The FHP model met in the hydrodynamic limit, the Navier -Stokes equation.