A fractional approach to fluid flow and solute transport within deformable saturated porous media

The non-Darcian flow and solute transport in geometrically nonlinear porous media are modeled with Riesz derivative solved via Simpson’s rule or treated through the Grünwald–Letnikow definition and subsequently discretized via Finite Difference schemes when considering anomalous diffusion, nonlinear diffusion, or anomalous solute advection–dispersion, respectively. Particularly, the standard diffusion and advection–dispersion equations are converted into fractional equations to take into account memory effects as well as non-Fickian dispersion processes. Hence, a 3D hydro-mechanical model accounting for geometric nonlinearities is correspondingly developed including the fractional diffusion–advection–dispersion equations (FRADEs) and a series of one-dimensional analyses are performed with validation purposes.