Chapter 10 - Lattice gas simulations

Summary

One of our main objectives has been to show that single-species non-thermal lattice gases can exhibit large-scale collective behavior governed by the same continuous, isotropic and Galilean-invariant equations as real Newtonian fluids. This is true despite the intrinsically Boolean, spatially discrete, anisotropic and non-Galilean invariant structure of lattice gases. Moreover, in the past 10 years, further lattice gas models have been designed to incorporate more complicated physical features such as reactive processes, magneto-hydrodynamic phenomena or surface tension (see Section 11.4 in Chapter 11).

On one hand, there has been considerable effort in basic research to understand the subtleties of the statistical mechanics of lattice gases and on the other hand intense work has been accomplished to take advantage of the similarities between lattice gases and real fluids in order to simulate fluid motions with simple and easily implemented lattice gas algorithms. Indeed, because of their fully Boolean cellular automaton structure, lattice gases are excellent candidates for efficient implementations on both dedicated and general purpose computers with serial, vectorial, parallel or even massively parallel architecture. In addition, various physical effects can be added at low cost. For example, the presence in a flow of a rigid fixed obstacle is extremely easy to take into account: it just requires replacing the standard collision rule by a bounce-back rule (see Section 2.4.1) on all nodes covered by the obstacle. Modifying the shape or the position of the obstacle is almost immediate, and no mesh modification is necessary.