2D cellular automata for turbulent convection

A cellular automaton (CA) formulation is devised to simulate 2-dimensional Rayleigh-Benard convection. The model is tested in the case of a standard plane-parallel shallow configuration for which analytical solutions of the hydrodynamical formulation are available at low enough Rayleigh numbers. If we use a measure of the intensity of gravity, k, as our free parameter (the analogue of the Rayleigh number), all other model parameters being fixed, then we can reproduce the well-known stationary roll-pattern predicted by the hydrodynamic theory at low k values. At higher k values the model exhibits a nonstationary turbulent flow pattern. Our formulation is extended to less trivial geometries for which an analytic treatment in the usual hydrodynamic context is not feasible. Besides geometry-constrained stationary patterns of motion in a range of low k values, this model exhibits again turbulent motions at higher k values