Numerical modeling of flow in porous media via lattice Boltzmann and discrete element methods

This paper aims to perform a two-dimensional study of flow in porous media through the implementation of a computational code based on the Lattice Boltzmann and Discrete Element methods, coupled using the immersed moving boundary technique. The Lattice Boltzmann Method employs a D2Q9 lattice and both BGK and MRT collision operators, while the Discrete Element Method is implemented using a linear interaction model between particles. The code was validated using classical benchmark problems, including the lid-driven cavity flow and fluid flow around a circular cylinder. Simulations were carried out for porous media composed of disk-shaped particles with uniform and random distributions, as well as realistic particle geometries. The formation of preferential flow paths was investigated, and the numerical permeability obtained from the simulations was compared with the Ergun and Kozeny–Carman equations, showing excellent numerical agreement. The results demonstrate that the developed code is a robust and efficient tool for simulating fluid–solid interactions in porous media.