Smooth particle hydrodynamics simulations of low Reynolds number flows through porous media

In this paper, a three-dimensional smooth particle hydrodynamics (SPH) simulator for modeling grain scale fluid flow in porous media is presented. The versatility of the SPH method has driven its use in increasingly complex areas of flow analysis, including the characterization of flow through permeable rock for both groundwater and petroleum reservoir research. SPH provides the means to model complex multi-phase flows through such media; however, acceptance of the methodology has been hampered by the apparent lack of actual verification within the literature, particulary in the three-dimensional case. In this paper, the accuracy of SPH is addressed via a comparison to the previously recognized benchmarks of authors such as Sangani and Acrivos (Int. J. Multiphase Flow 1982; 8(4): 343–360), Zick and Homsy (J. Fluid Mech. 1982; 115:13–26) and Larson and Higdon (Phys. Fluids A 1989; 1(1):38–46) for the well-defined classical problems of flow through idealized two- and three-dimensional porous media. The accuracy of results for such low Reynolds number flows is highly dependent on the implementation of no-slip boundary conditions. A new, robust and numerically efficient, method for implementing such boundaries in SPH is presented. Simulation results for friction coefficient and permeability are shown to agree well with the available benchmarks