A Compatible Single-Phase/Two-Phase Numerical Model: 1. Modeling the Transient Salt-Water/Fresh-Water Interface Motion

Abstract A numerical model (NEWVAR) to simulate the transient movement of a discrete interface between salt water and fresh water has been developed. NEWVAR is designed to allow the analysis of a regional two-dimensional ground-water flow in coastal aquifers. The numerical solution permits the prediction of both regional fresh-water levels and two-dimensional fresh-water/salt-water interface by using nested square meshes.
The numerical solution is based on the finite-difference method; the Gauss-Jordan direct method is used for solving steady- and unsteady-state linear equations. Different procedures are used to avoid numerical difficulties in the transient position of the interface toe for two-dimensional areal flow.
The numerical solution was tested against the analytical ones for the cases of an advancing interface and of a floating fresh-water lens over sea water. These tests showed good agreement, thus verifying the finite-difference approximation. The results of an application of this model to a real aquifer are discussed in a companion paper entitled: "A Compatible Single-Phase/Two-Phase Numerical Model 2. Application to a Coastal Aquifer in Mexico."