MATLAB Implementation of 2D D2Q9 Lattice Boltzmann Method for Flow Around a Cylinder

This project implements a MATLAB simulation of fluid flow around a cylindrical obstacle using the Lattice Boltzmann Method (LBM) with a D2Q9 lattice structure. The core implementation involves setting up the 2D grid with nine discrete velocity directions (D2Q9), where key functions handle particle distribution evolution through collision and streaming steps. The algorithm calculates equilibrium distribution functions using local density and velocity fields, followed by a relaxation process toward equilibrium using the BGK approximation. Boundary conditions are carefully implemented, including bounce-back schemes for the cylinder surface and periodic or fixed conditions for domain boundaries. The simulation tracks macroscopic variables (density, velocity) by moments of distribution functions, allowing analysis of flow parameters such as Reynolds number (controlled via relaxation time) and cylinder diameter effects. The code structure includes initialization routines, main time-stepping loops with collision-streaming operations, and visualization modules for flow field analysis. This implementation provides insights into both fluid dynamics principles and computational methods for solving the Navier-Stokes equations through mesoscopic particle interactions.