Lattice Boltzmann Method with D2Q9 Implementation

This article explores the application of Lattice Boltzmann Method (LBM) with a D2Q9 MATLAB implementation for fluid dynamics simulation. The Lattice Boltzmann Method is a computational fluid dynamics approach based on microscopic particle behavior. The D2Q9 model refers to the discretization of fluid distribution functions into 9 directions within a two-dimensional space. The MATLAB program implements collision and streaming processes through key functions that handle particle distribution evolution. The core algorithm utilizes a double distribution function approach where the program maintains separate arrays for each discrete velocity direction. Key parameters controlling fluid velocity and density can be modified through variables like relaxation time (tau) and initial density conditions. This implementation simulates fluid movement in two-dimensional space and allows for the investigation of velocity fields and pressure distributions. The code structure includes initialization routines for setting up lattice constants, collision operators implementing the BGK approximation, and boundary condition handlers for various flow scenarios. Through parameter adjustment, users can study different fluid behaviors and visualize results using built-in plotting functions for velocity vectors and pressure contours.