Saltwater intrusion into coastal aquifers is a major environmental problem faced by coastal regions around the world. As the population in these areas continues to grow, efficiently managing the water resources will become increasingly more difficult. Numerical models have contributed immensely in aiding water resource managers to better plan for the future by predicting the results of various environmental scenarios. Saltwater intrusion problems are solved using variable density numerical models. However, these models have to be validated against known solutions in order to test their applicability in solving these specific problems.

Variable density models have been widely tested by using the Henry problem (1960). Henry converted a hypothetical saltwater intrusion case into dimensionless parameters and used the Galerkin method to derive a semi-analytical solution. However, researchers have reported numerous problems with this solution. One of the problems is that the solution does not converge for generic values of the dimensionless parameters. The test case solved by Henry was also criticized for being insensitive to density coupling effects (Simpson and Clement, 2003).

In our analysis, we will investigate different analytical solution techniques which can be utilized to solve the Henry-type problem. This work would greatly benefit the variable density modeling community by providing them with a robust solution to the saltwater intrusion problem which can then be used as an alternative benchmarking problem. The presentation would focus on describing Henry’s solution technique which, although not trivial, is based on a simple problem definition. We would then show a detailed mathematical analysis of some other solution techniques and discuss their respective limitations. In the end, the solutions from these methods would be compared against each other and against the numerical solutions.