Buoyant Mixtures of Cellular Automaton Gases
Christopher Burges
Stéphane Zaleski
Department of Mathematics, Massachussets Institute of Technology,
Cambridge, MA 02139, USA
Abstract
The use of lattice gas (cellular automaton) models has recently been advocated as an interesting method for the simulation of fluid flow. These automata are an idealization of the real microscopic molecular dynamics. We present a model derived from the hexagonal lattice gas rules of Frisch Hasslacher and Pomeau (FHP) that incorporate buoyant forces and discusses its properties. We derive the hydrodynamical equations in the low density limit and find the buoyant force and seepage effects characteristic of gravitating mixtures, as well as deviations from the Navier Stokes equations in the compressible case. An equivalent of the quasi-incompressible limit of Boussinesq exists, where the Boussinesq equations are recovered but only for steady flow. The unsteady flow equations suffer from the lack of Galilean invariance of FHP type models. We discuss other tentative models that would overcome this difficulty. The self-diffusion coefficient is also computed from the theory, as as well as the mean free path. This allows one to check some of the predictions of the Chapman-Enskog expansion for these gases. We also perform numerical simulations at a Rayleigh number of 6000, showing natural convection near a heated wall and the Rayleigh-Benard instability in a time independent regime.
