Buoyant Mixtures of Cellular Automaton Gases

The use of lattice gas (cellular automaton) models has recently been advocated as an interesting method for the simulat ion of fluid flow . Th ese automata are an idealizat ion of the real microscopic molecula r dynamics. We present a model derived from the hexagonal lat t ice gas ru les of Frisch Hasslacher and Pomea u (FHP) that incorporates buoyant forces and d iscusses its prope rt ies. We der ive the hydr odyn amical equations in the low de nsity limit and find the buoyant force and seepage effects characte ristic of gravit at ing mixtu res, as well as deviations from the Navier Stokes equations in the compressible case. An equivalent of the qu asi-incompr essible limit of Boussinesq exists , where th e Boussinesq equa tions are recovered bu t only for steady flow. The unsteady flow equ ation s suffer from the lack of Galilean invari ance of FHP type models. We discuss ot her tentative models that would overcome this difficu lty. T he self-d iffusion coefficient is also comp uted from the theory, as well as t he mean free path . T his allows one to check some of t he pred ictions of the ChapmanEnskog expansion for t hese gases . We also perfor m nume rical simulations at a Rayleigh number of 6000, show ing natura l convection nea r a heat ed wall and t he Ray leigh-Benard instability in a time ind ependent regime.