A Generalized Approach for Modeling 3D Transient Free and Moving Boundaries in Coastal Aquifers

Coastal aquifers involve varying conditions in time and space, owing to the occurrence of free and moving boundaries, such as the water table, seepage face and saltwater intrusion interface. A fast Updating Procedure (FUP) is developed for solving these interfaces in steady and transient conditions with the finite element method. Several test examples, which involve confined and phreatic groundwater flow in coastal aquifers, are studied to demonstrate the FUP capability of predicting accurate results. Comparisons of the FUP numerical results are made against available analytical solutions, laboratory experiments measurements and other computer codes. To show also the capability of this technique to solve real field situations, it was applied to the coastal aquifer of Martil in Morocco to study and understand the aquifer response to changes in recharge and total rate of pumping water, and their effects on seawater intrusion. INTRODUCTION The problem of saltwater intrusion can be treated with two methods, one considers that saltwater and freshwater are miscible and that a transition zone exists [Voss, 1984], in which situation miscible density dependent groundwater flow models are traditionally used. The other method is based on an abrupt approximation [Bear, 1972; Huyakorn et al., 1996; Larabi and De Smedt, 1997; Sbai, 1999] and for which (i) the transition zone is thin relative to the thickness of the freshwater lens, (ii) freshwater and saltwater are immiscible, and (iii) the freshwater and saltwater are separated by a sharp interface. Additionally, the approach considering flow in both fresh and salt water regions, leads to a coupled system of equations to be solved. This is cumbersome for a fully three dimensional model owing to numerical constraints and higher computational costs involved. Instead, a new numerical procedure is developed, assuming a sharp interface between freshwater and saltwater, for which the location, shape and extent must be determined. A first steady state version of this model was presented by [Larabi and De Smedt, 1997], who elaborate a part of the numerical technique which will be described, and also validate the developed model by running several benchmarks. In this work an enhanced version of their steady state model is developed, several features were implemented as a robust solver based on an M-matrix preconditioned incomplete factorization. Also, special boundary conditions such as the seepage face, and sea outflow face are efficiently handled. But, the most important achievement is the development of a transient model for simulating the moving sharp interface and the moving water table in case of free surface flow conditions. Numerical algorithms used