Numerical SPH Calculations of Fluid Flow Through Saturated and Non-saturated Porous Media

The fluid flow through saturated and non-saturated homogeneous porous media is studied numerically using a modified version of a Smoothed Particle Hydrodynamics (SPH) code. The modifications implemented in the original SPH code to model the incompressible flow at low Reynolds numbers through a porous medium are described. The performance of the model is demonstrated for three-dimensional flow through idealized porous media consisting of regular square and hexagonal arrays of solid spheres. For each of these configurations we consider a set of flow calculations through saturated and non-saturated porous matrices differing in the magnitude of the \(z\)-component of the hydraulic gradient. For the saturated case, the Darcy’s law is recovered and the hydraulic conductivity is calculated for both geometries. The numerical results are consistent with previous two-dimensional simulations in that the square case has a lower hydraulic conductivity than the hexagonal case. Finally, for the non-saturated case the relaxation time is calculated for different body forces. In this case, the system never reaches steady-state conditions.