Thermal cellular automata fluids

Abstract

The concepts of local temperature and local thermal equilibrium are introduced in the context of lattice gas cellular automata (LGGAs) whose dynamics conserves energy. Green-Kubo expressions for thermal transport coefficients, in particular for the heat conductivity, are derived in a form, equivalent to those for continuous fluids. All thermal transport coefficients are evaluated in Boltzmann approximation as thermal averages of matrix elements of the inverse Boltzmann collision operator, fully analogous to the results for continuous systems, and fully model-independent. The collision operator is expressed in terms of transition probabilities between in- and out-states. Staggered diffusivities arising from spuriously conserved quantities in LGCAs are also calculated. Examples of models with either cubic or hexagonal symmetries are discussed, where particles may or may not have internal energies.