MATLAB Source Code for Fluid Simulation Using Lattice Gas Cellular Automata

Lattice Gas Automata (LGA) represents a fluid simulation method based on discrete particle dynamics, widely applicable in computational fluid dynamics. Implementing LGA simulation in MATLAB enables intuitive observation of microscopic dynamic behaviors in fluid flow.

Fundamental Principles The core concept of LGA involves discretizing fluid into particles that move on regular lattices (such as 2D hexagonal or square grids). Particles interact through simple collision rules, while macroscopically demonstrating behaviors consistent with the Navier-Stokes equations for viscous fluids. In code implementation, this requires defining discrete velocity sets (e.g., 9 directions in D2Q9 model) and implementing Boolean occupation arrays for particle distribution tracking.

Implementation Approach Grid Initialization: Construct 2D/3D lattice structures where each grid node stores particle velocity directions using matrix representations. For D2Q9 model, implement a 9-bit Boolean array per cell to track particle presence in each direction. Collision Phase: Apply preset collision rules (HPP or FHP models) using logical operations and bit manipulation. Ensure momentum conservation through carefully designed collision matrices that redistribute particles while preserving physical properties. Streaming Phase: Execute particle migration to adjacent nodes through matrix shifting operations along velocity directions. Implement circular shift functions (circshift in MATLAB) for efficient neighbor access and data transfer. Boundary Handling: Code reflection boundaries using conditional flipping of velocity components, periodic boundaries via modular arithmetic, and fixed boundaries through predefined state arrays. Statistical Observation: Calculate macroscopic quantities (density, velocity fields) through summation functions over direction arrays. Visualize results using MATLAB's quiver plots for velocity fields and contour maps for density distributions.

Extended Applications LGA's simplified rules make it suitable for parallel computing implementations using MATLAB's parallel toolbox. The framework can be extended to multiphase flow simulations by introducing additional particle types or complex boundary modeling through customized collision rules. While limited in computational accuracy, LGA serves as an excellent educational and research tool due to its conceptual transparency and straightforward implementation using matrix operations and logical indexing in MATLAB.