FHP model
The FHP model is a fundamental lattice gas model and a cellular automaton for simulation of gases and liquids . It is also known as Lattice Gas Cellular Automata (LGCA).
history
The FHP model was set up in 1986 by Uriel Frisch , Brosl Hasslacher and Yves Pomeau , whose initials give the model its name. With the HPP model by Hardy, Pomeau and de Pazzis from 1973 it has a historical forerunner. The reason for the comparatively long time of 13 years until further development is that the HPP model lacked isotropy as an important property and it was believed that such models could in principle not be isotropic. After the isotropy had been proven for the FHP model, an intensive study of the model and a number of variants quickly began. The discovery of isotropy in the FHP model in connection with the high computational efficiency led, on the one hand, to the fact that the FHP model was reported on the front page of the Washington Post , on the other hand, the model and any research on it had previously been considered secret and To classify militarily significant, thus to prevent publications .
model
As the name grid gas implies, the entire dynamic takes place on a grid . In the case of the FHP model, it is a grid of nothing but equilateral triangles. There is consequently a six-fold (discrete) rotational symmetry . The triangular grid is the key difference to the HPP model, which is based on an orthogonal grid (chessboard).
- Particles always only exist on the grid points, i.e. H. never on the edges and never on the surfaces.
- Each particle is assigned a direction (from one grid point to another immediately adjacent).
- A grid point can have a maximum of one particle for each direction, i.e. H. contain between zero and six particles in total.
- The particles are moved forward in rounds. A check is made between each move to determine whether there is a scatter at a grid point.
Scattering : Scattering occurs when there are two, three or four particles on a grid point at the same time, the momentum (directions) of which add up to zero. With two particles this means that the particles have to have opposite directions, with three that the angles between the particles have to be 120 ° and with four particles that the unoccupied directions have to be opposite. When two particles are scattered, both directions are rotated by 60 ° to the right or to the left, whereby the direction of the deflection is chosen randomly and with the same probability (50:50). If three particles are scattered, occupied and unoccupied directions are exchanged, and if four particles are scattered, the unoccupied direction is rotated 60 ° to the right or left. In any case, the pulse sum is zero even after the scatter. In this way, the conservation of momentum is guaranteed in the entire model - apart from edge effects . In a deterministic version of the model, the direction of deflection is not decided at random, but deflected alternately to the right and left. In this case, the same initial conditions always result in the same simulation sequence.
See also the simulation implemented in NetLogo .
properties
The FHP model fulfills the Navier-Stokes equation in the hydrodynamic limit case .
literature
- J. Hardy, Y. Pomeau, O. de Pazzis: Time Evolution of a Two-Dimensional Classical Lattice System . In: Physical Review Letters. 31, 1973, ISSN 0031-9007 , pp. 276-279, doi: 10.1103 / PhysRevLett.31.276 .
- U. Frisch, B. Hasslacher, Y. Pomeau: Lattice-Gas Automata for the Navier-Stokes Equation . Physical Review Letters. 56, 1986, pp. 1505-1508, doi: 10.1103 / PhysRevLett.56.1505 .
- DH Rothman, S. Zaleski: Lattice gas cellular automata: simple models of complex hydrodynamics . Cambridge University Press, Cambridge et al. 1997, ISBN 0-521-55201-X .
Individual evidence
- ↑ Ethan Bakshy: NetLogo Models Library: Lattice Gas Automaton. Retrieved November 27, 2018 .