Lattice Boltzmann Method for Two-Phase Flow Simulation with MATLAB Implementation

The lattice Boltzmann method is a widely used numerical technique for simulating two-phase flow systems. This mesoscopic approach operates between molecular dynamics and continuum mechanics, utilizing particle distribution functions to model fluid behavior. A typical MATLAB implementation involves two key algorithmic components: collision and streaming operations. The collision step calculates new distribution functions using the Bhatnagar-Gross-Krook (BGK) approximation, while the streaming phase propagates these distributions to neighboring lattice nodes. MATLAB programs for lattice Boltzmann two-phase flow simulations commonly implement multi-phase models such as the Shan-Chen model, which incorporates inter-particle forces through potential functions. Key MATLAB functions often include lattice initialization routines, boundary condition handlers (bounce-back, periodic), and phase-field calculation modules. These programs can effectively model various two-phase phenomena including capillary flows in porous media, droplet dynamics in biological systems, and multiphase interactions in industrial processes. The MATLAB implementation typically organizes the computation into discrete time steps, where each iteration updates distribution functions across a structured grid. Common code structures feature matrix operations optimized for MATLAB's vectorized computation, with separate functions handling fluid properties, interaction potentials, and visualization outputs. Through parameter customization in the MATLAB code, researchers can simulate different viscosity ratios, density contrasts, and surface tension effects, providing valuable insights for optimizing complex multiphase systems.