Monte Carlo Lattice Gas for Fluctuating Fluids

For small fluid systems (or close to a critical point) fluctuations are important in fluids. The reason for fluctuations can be traced back to the fact that nature is discrete. However, the current mainstream fluid simulation models do not have an ideal answer for fluctuations. The lattice Boltzmann, for example, needs fluctuations to be added externally using a Langevin approach. 

Lattice gas methods are inherently noisy, and a lot of work analyzing fluctuating systems was pe rformed with them. Their non-noisy limit, the lattice Boltzmann method, eventually replaced these hydrodynamic lattice gas methods because certain artifacts of the original Boolean lattice gases could be overcome. We have been able to show that integer lattice gases can be constructed that are equivalent to the lattice Boltzmann method. These lattice gases offer both inherent fluctuations and unconditional stability that lattice Boltzmann lacks.

We present here an efficient integer lattice gas method based on distribution sampling for the hydrodynamic regime, allowing hydrodynamic systems to now be simulated with inherent fluctuations at a numerical cost comparable to lattice Boltzmann methods.