Mesoscale SPH modeling of fluid flow in isotropic porous media

A novel numerical technique—Smoothed Particle Hydrodynamics (SPH) is used to model the fluid flow in isotropic porous media. The porous structure is resolved in a mesoscopic-level by randomly assigning certain portion of SPH particles to fixed locations. A repulsive force, similar in form to the 12-6 Lennard-Jones potential between atoms, is set in place to mimic the interactions between fluid and porous structure. This force is initiated from the fixed porous material particle and may act on its nearby moving fluid particles. In this way, the fluid is directed to pass through the porous structure in physically reasonable paths. For periodic porous systems formed by intersecting solid material with straight parallel fluid channels, the Kozeny formula of permeability was reproduced successfully, which, to a great extent, validates the reliability of the developed SPH model. Further, SPH simulations for the fluid flows induced by an applied streamwise body force in two-dimensional porous structures of different porosities are performed. The macroscopic Darcy's law is confirmed to be valid only in the creeping flow regime. The derived relationship of permeability versus porosity is compared with some existing numerical results/experimental data, which demonstrates that the present SPH model is able to capture the essential features of the fluid flow in porous media.