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

The Lattice Boltzmann LBE model serves as a computational method for simulating fluid dynamics, widely applied in porous media flow and related domains. For its implementation in two-dimensional porous media fluid seepage, the approach involves defining appropriate geometric configurations while employing the D2Q9 lattice structure (featuring nine discrete velocity directions) and BGK (Bhatnagar-Gross-Krook) collision model. The core algorithm typically includes stream and collision steps, where particle distribution functions propagate along lattice directions and undergo relaxation toward equilibrium states. This model effectively handles complex boundary conditions through bounce-back schemes for solid obstacles and can simulate various fluid mechanics phenomena including fluid motion, heat transfer, mass transport, and phase transitions. Consequently, the Lattice Boltzmann LBE model demonstrates extensive applicability in both scientific research and engineering practices, particularly for pore-scale simulations where traditional Navier-Stokes solvers face limitations. Key implementation aspects involve optimizing memory allocation for distribution functions and leveraging parallel computing for large-scale simulations.