Derivation of a Sharp-Diffuse Interfaces Model for Seawater Intrusion in a Free Aquifer. Numerical Simulations

We derive a new model for seawater intrusion phenomena in free aquifers. It combines the efficiency of the sharp interface approach with the physical realism of the diffuse interface one. More precisely, a phase field is used as an intermediate variable for including the exchanges between the characteristic layers of the aquifer (salt water, fresh water, unsaturated zone). The threedimensional problem is reduced to a two-dimensional model involving a strongly coupled system of PDEs of parabolic type describing the evolution of the depths of the two free surfaces. The model is discretized by finite elements in space and by a semi-implicit Euler method in time. Numerical simulations present some physical predictions from the model.