Lattice Boltzmann scheme with real numbered solid density for the simulation of flow in porous media

A modified lattice Boltzmann scheme for the simulation of flow in porous media is introduced, where momentum loss due to the presence of solid obstacles to flow is incorporated into the evolution equation. A real numbered parameter specified at each lattice node is related to the density of solid scatterers and represents the effect of porous medium solid structure on hydrodynamics. This scheme removes both the need for spatial and temporal averaging and the microscopic length scales associated with important classes of porous media. A numerical study demonstrates the adherence of the approach to the Navier-Stokes equation with an effective damping term. The potential use of the scheme to aid permeability predictions in realistic geological materials is discussed.