Modeling Sea‐Water Intrusion with Open Boundary Conditions

Abstract

AbstractThe present study concerns the application of a new numerical approach to describe the fresh‐water /sea‐water relationships in coastal aquifers. Essentially, a solution to the partial differential equation governing the regional motion of a phreatic surface and the resulting interface between fresh water and salt water is analyzed by a Galerkin finite‐element formulation. A single‐phase steady numerical model was applied to approximate, with simple triangular elements, the regional behavior of a coastal aquifer under appropriate sinks, sources, Neumann, outflow face, and open boundary conditions. On the one hand, outflow open boundaries at the coastline were not treated with other classical boundary conditions (Dirichlet or the outflow face approach), but instead with a formal numerical approach for open boundaries inspired in this particular case by the Dupuit approximation of horizontal outflow at the boundary. The solution to this numerical model, together with the Ghyben‐Herzberg principle, allows the correct simulation of fresh‐water heads and the position of the salt‐water interface for a steeply sloping coast. Although the solutions were precise and do not present classical numerical oscillations, this approach requires a previous solution with Dirichlet boundary conditions at the coastline in order to find a good convergence of the solution algorithm. On the other hand, the same precise results were obtained with a more restrictive open boundary condition, similar in a way to the outflow face approach, which required less computer time, did not need a prior numerical solution and could be extended to different coastline conditions. The steady‐state problem was solved for different hypothetical coastal aquifers and fresh‐water usage through three types of numerical tests. Calculated fresh‐water heads, interface positions and discharges show very precise results throughout the domain and especially at the coastline when compared to analytical, experimental, and numerically correct solutions. Therefore, interface positions, fresh‐water heads, and discharges originating from the steady regional behavior of coastal aquifers can be precisely predicted by numerical modeling when open boundaries towards the sea are properly treated for the likely conditions of the coastline.