Simulation of Salt‐Water Interface Motion

ABSTRACT A numerical model is presented that solves the partial differential equations describing the motion of salt water and fresh water separated by a sharp interface. The areal equations are based on the Dupuit approximation and are obtained from partial integration over the vertical dimension. Finite‐difference techniques are applied and the utility of several solution schemes is tested. The most efficient and accurate solution scheme uses block line‐successive over‐relaxation. Examples are given to: (1) test the model, (2) evaluate the Dupuit approximation, and (3) demonstrate the application to a field situation. The results show that the model is in good agreement with an analytical solution, but under severe conditions the Dupuit approximation may be inappropriate. The model is applied to a field area near Kahului, Maui, Hawaii and results extend the analysis of the problem beyond previous efforts.