Application of Lattice Boltzmann LBE Model in Two-Dimensional Porous Media Flow Simulation

The Lattice Boltzmann Method (LBM), as a mesoscopic-scale fluid simulation approach, has demonstrated unique advantages in porous media flow studies in recent years. Its core concept involves tracking the evolution of fluid particle distribution functions through discrete velocity models, rather than directly solving macroscopic Navier-Stokes equations.

In two-dimensional porous media flow scenarios, the D2Q9 model serves as the most commonly used discrete velocity scheme. This model defines nine discrete velocity directions (including stationary particles) and accurately reproduces mass conservation and momentum transport processes. The BGK (Bhatnagar-Gross-Krook) collision model, as the classic simplified operator, controls the system's approach to local equilibrium through a single relaxation time parameter τ.

This method breaks through the grid limitations of traditional CFD and naturally adapts to complex geometric boundaries of porous media. When handling solid-pore interfaces, the bounce-back boundary condition efficiently implements no-slip boundary effects. By adjusting relaxation parameters and porosity, the method can simulate various flow regimes from low-velocity Darcy flow to non-Darcy flow considering inertial effects.

Compared to conventional methods, LBM exhibits three distinctive features in porous media simulation: simplified microscopic boundary treatment, high parallel efficiency, and natural coupling of pore-scale effects. These characteristics make it an essential tool for microscopic mechanism studies in fields such as petroleum extraction and groundwater contamination transport.