Numerical Approach of a Water Flow in an Unsaturated Porous Medium by Coupling Between the Navier–Stokes and Darcy–Forchheimer Equations

In the present research, simulations have been conducted to determine numerically the dynamic behaviour of the flow of underground water fed by a river. The basic equations governing the problem studied are those of Navier–Stokes equations of conservation of momentum (flows between pores), coupled by the Darcy–Forchheimer equations (flows within these pores). To understand the phenomena involved, we first study the impact of flow rate on the pressure and the filtration velocity in the underground medium, the second part is devoted to the calculation of the elevation effect of the river water on the flow behaviour in the saturated and unsaturated zone of the aquifer.