Early Attempts With A Square Lattice
In papers published in 1973 and 1976, Hardy, Pomeau and de Pazzis introduced the first Lattice Boltzmann model, which is called the HPP model after the authors. In this model, the lattice is square, and particles can move to any of the four sites whose cells share a common edge. Particles cannot move diagonally.
If two particles collide head-on, for example a particle moving to the left meets a particle moving to the right, the outcome will be two particles leaving the site at right angles to the direction they came in.
The HPP model lacked rotational invariance, which made the model highly anisotropic. This means for example, that the vortices produced by the HPP model are square-shaped.
Read more about this topic: Lattice Gas Automaton
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