Lattice Boltzmann Method for Porous Media Flow Simulation

The Lattice Boltzmann Method program is widely employed for simulating fluid flow through porous media. It utilizes the D2Q9 computational model which transforms complex fluid dynamics phenomena into simplified collision and streaming processes. The implementation typically involves discrete velocity directions with equilibrium distribution functions governed by local conservation laws. Through this approach, researchers can gain deeper insights into fluid transport behaviors in porous structures, supporting applications in hydrogeology, petroleum engineering, and environmental engineering. The method's computational efficiency stems from its local operations and inherent parallelizability, with key functions including density/pressure calculation through particle distribution summation and velocity field computation via momentum exchange. These characteristics have led to widespread adoption in engineering practice, particularly for handling complex geometries through bounce-back boundary conditions and incorporating multi-relaxation-time schemes for enhanced stability.