A GALILEAN-INVARIANT IMMISCIBLE LATTICE GAS

Recently, lattice-gas methods have been introduced as a technique for the simulation of one- and two-phase fluid flow. These methods model the fluid as a collection of particles which propagate on a regular lattice and undergo collisions at the nodes of the lattice. In an asymptotic limit, lattice gases simulate the Navier-Stokes equations. However, these models suffer from a lack of Galilean invariance. An important physical manifestation of the lack of invariance is that the fluid vorticity advects with a velocity different from the velocity of the fluid. We introduce a new, Galilean-invariant, model for simulating immiscible two-phase flow. Unlike previous Galilean-invariant models, the collisions in this new model satisfy semi-detailed balance, which is achieved by the inclusion of a large number of rest particles with zero velocity. Since adding many rest particles is not computationally tractable, the presence of a large number of such particles is simulated by weighting the outcome of the collisions by a factor related to the frequency with which the collisions would have occurred if the rest particles had been explicitly included in the model. We demonstrate that, in the new model, the vorticity advects at the same velocity as the fluid. We also show that the model obeys Laplace's formula for surface tension and demonstrate an application of the new model to the Rayleigh-Taylor instability. Growth rates as a function of wavenumber computed in the early stages of the instability compare well to theoretical predictions.