Convergence and long time behavior of a Finite Volume scheme for an isotropic seawater intrusion model with a sharp-diffuse interface in a confined aquifer.
Ahmed Ait Hammou Oulhaj, David Maltese, N. Staïli · HAL (Le Centre pour la Communication Scientifique Directe) · 2020
We study and simulate a sharp-diffuse interface model in the context of seawater intrusion in an isotropic confined aquifer. It is a strongly coupled system of partial differential equations which include elliptic and par-abolic equations modelling the flow of fresh and saltwater. We study a finite volume scheme. This scheme ensures a discrete maximum principle for the discrete solution without any restriction on the transmissibility coefficients. Moreover it also provides a control on the entropy. The existence of a discrete solution and the convergence of this scheme are obtained, based on nonlinear stability results. The temporal decay rates for convergence of the discrete solution to the homogeneous steady state is shown using a discrete logarithmic Sobolev inequality. Finally, we propose a numerical simulations to illustrate the behavior of the model and of the scheme.