Introduction

The Lattice Boltzmann Method (LBM) has emerged as a powerful alternative to traditional computational fluid dynamics (CFD) approaches. Unlike conventional methods that directly solve the Navier-Stokes equations, LBM is based on kinetic theory and statistical physics, offering a unique perspective on fluid dynamics simulation.

Theoretical Foundation

The Boltzmann Equation

At the heart of LBM lies the Boltzmann equation, which describes the evolution of a particle distribution function f(x, ξ, t):