Motion of the Seawater Interface in Coastal Aquifers: A Numerical Solution

Abstract

The partial differential equations that describe the motion of the seawater interface and the free surface in a phreatic coastal aquifer (or the freshwater head replacing the latter, in the confined case) are presented. They are based on the Dupuit approximation and take into consideration the geometry of the vertical section through the aquifer, in whose plane the flow takes place, as well as the spatial variation of properties of the porous medium and the spatial and temporal distributions of accretion, recharge, and pumping. An implicit numerical scheme is presented to solve the set of simultaneous partial differential equations. The scheme is based on a linearization of the equations and employs a grid with one spacing over the intrusion length and a different spacing in the remainder of the field. Efficient solution of the resulting set of simultaneous linear equations for each time step is achieved by arranging them in a way that results in a 7 diagonal coefficient matrix. Examples are presented, for which the numerical solutions are compared with analytical solutions or laboratory experiments.