Boundary element computation of fresh water groundwater lenses

Abstract

Groundwater is often used as a source of potable water on tropical islands. Boundary integral techniques are used here to determine the shape of the fresh water lens floating over intruded salty groundwater beneath a two dimensional tropical island. These computations may be used to determine optimum well location and maximum pumping rates. This paper describes the application of boundary integrals to groundwater flow and discretisation of the integral for numerical evaluation. Solutions to some numerical difficulties encountered in this problem are presented. These include a pseudo-unsteady method of satisfying the highly nonlinear boundary conditions that define the salt-fresh water interface beneath and phreatic surface above the lens, and reduced element requirements by the use of a suitable Green's function to represent the outflow surfaces at the sides of an island with sloping sides, obtained by conformal mapping. Finally, some results are presented and other applications are briefly discussed.