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

Catherine Choquet (1) , Moussa Mory Diédhiou (1) , Carole Rosier (2)

1 MIA - Mathématiques, Image et Applications - EA 3165
2 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

We derive a new model for seawater intrusion phenomena in free aquifers. It com- bines 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 three- dimensional 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.

Mots clés: seawater intrusion; free boundaries; nonlinear parabolic PDE; system of strongly coupled PDEs; numerical simulations; finite elements

Domaines: Equations aux dérivées partielles [math.AP]

Catherine Choquet, Moussa Mory Diédhiou, Carole Rosier. Derivation of a Sharp-Diffuse Interfaces Model for Seawater Intrusion in a Free Aquifer. Numerical Simulations. SIAM Journal on Applied Mathematics, 2016, ⟨10.1137/15M102099X⟩. ⟨hal-01273800⟩