Derivation of Seawater Intrusion Models by Formal Asymptotics

Abstract

In this paper, we consider the flow of fresh and saltwater in a saturated porous medium in order to describe the seawater intrusion. Starting from a formulation with constant densities respectively of fresh and saltwater, whose velocities are proportional to the gradient of pressure (Darcy's law), we consider the formal asymptotic limit as the aspect ratio between the thickness and the horizontal length of the porous medium tends to zero. In the limit of the regime defined by the Dupuit-Forchheimer condition, we identify reduced models of Boussinesq type both in the cases of unconfined and confined aquifers. MSC: 35R35, 35B40

Existence result for degenerate cross-diffusion system with application to seawater intrusion

“…We assume that in the porous medium, the interface between the saltwater and the bedrock is given as {z = 0}, the interface between the saltwater and the freshwater, which are assumed to be unmiscible, can be written as {z = g(t, x)}, and the interface between the freshwater and the dry soil can be written as {z = h(t, x) + g(t, x)}. Then the evolutions of h and g are given by a coupled nonlinear parabolic system (we refer to see [16]) of the form h t = div {h∇(ν(h + g))} in Ω T , g t = div {g∇(νh + g)}…”

Assessing the Contribution of Demographic Growth, Climate Change, and the Refugee Crisis on Seawater Intrusion in the Tripoli Aquifer

“…The second one is based on the principle of hydrodynamic dispersion in porous media, where a transition zone exists between fresh and sea water [19]. Here, we use a mathematical model based on the 2D sharp interface approach [13,14] in homogeneous medium. In the work of Kalaoun et al [12], the mathematical and numerical model of the seawater intrusion in the Tripoli aquifer was described supposing the steady state and an unconfined aquifer.…”

“…The mathematical model was based on the sharp interface approach. In this approach [13,14], the model is obtained using Darcy's law combined with the mass conservation law in freshwater and seawater zones. A system of Equations (1) and (2) derives from this combination.…”

Numerical analysis of a finite volume scheme for a seawater intrusion model with cross‐diffusion in an unconfined aquifer

“…In this article, we consider the first approach, by focusing on the seawater intrusion model in an unconfined aquifer, obtained in considering the formal asymptotic limit as the aspect ratio between the thickness and the horizontal length of the porous medium tends to zero. In our setting ξ is a nonnegative function expressing the height of the interface between the saltwater and the freshwater while is the height of the interface separating the freshwater and the dry soil.…”