Abstract
The direct numerical simulation (DNS) is an effective and useful tool in the two-phase fluid flow studying. The projection method on the staggered grid was applied in this paper to solve the incompressible Navier-Stokes equations in irregular domains at the pore-scale level (irregular boundary is presented by its level-set function). The permeability of porous medium which was constructed by the random positioning of penetrable spheres of equal radii were numerically calculated and validated by comparing with theoretical estimations of permeability based on the numerical solution of the lattice-Boltzmann equation in irregular domains in previous works. All numerical calculations were performed using PARIS simulator.