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.