Lattice Gas Cellular Automata Fluid Dynamics Case Study

The Navier-Stokes equations are the basis for describing the flow of a viscus material and are used to model fluid motion from weather to air flow over a wing. These equations, however, tend to be notoriously difficult to solve, whether analytically or computationally, even for small systems due to their highly nonlinear nature. Thus, less complicated methods that are more computationally tractable are desirable in domains as varied as hydroelectric power to race car construction. At a fundamental level, fluids are composed of interacting molecules. Lattice Gas Cellular Automata (LGCA) represents an efficient way to simulate these interacting fluid particles on a lattice. LGCA captures the microscopic behavior of the fluid by applying simple collision and propagation rules at each lattice site. This leads to realistic macroscopic behavior that can be used to build insight about real fluid flow. Here, we show the Hardy, Pomeau, and de Pazzis model for simulating a lattice gas. The computational framework presented in this case study can also be expanded to more complicated LGCA.