Modelling of non-Darcy flows through porous media using extended incompressible smoothed particle hydrodynamics

In this article, a novel numerical method is presented for the simulation of non-Darcy flows through porous media by the incompressible smooth particle hydrodynamics (ISPH) method with a predictor-corrector scheme. In the ISPH algorithm, a semi-implicit velocity-correction procedure is used and the pressure is obtained by solving the pressure Poisson equation. The key point for the application to non-Darcy flows is to include porosity and drag forces of the medium (the Darcy term and the Forcheimer term) in the ISPH method. Unsteady lid-driven flow, natural convection in non-Darcy porous cavities, and natural convection at a porous medium-fluid interface are examined separately by our extended ISPH method. The results are presented with flow configurations, isotherms, and average Nusselt numbers for different Darcy numbers from 10^-4 to 10^-2, porosity values from 0.4 to 0.9, and Reynolds/Rayleigh numbers. The flow pattern and rate of heat transfer inside the cavity are affected by these parameters. The results demonstrate the important effect of the Darcy number on both the heat transfer rate and the flow regime. The results from this investigation are well validated and compare favorably with previously published results.