Approximate Solutions for Horizontal Unconfined Aquifers in the Buildup Phase

Abstract

We construct approximate analytical solutions of the Boussinesq equation for horizontal unconfined aquifers in the buildup phase under constant recharge and zero-inflow conditions. We employ a variety of methods, which include wave solutions, self-similar solutions, and two classical linear approximations of the Boussinesq equation (linear and quadratic), to explore the behavior and performance of the solutions derived from each method against the Boussinesq equation and the exact (non-closed form) analytical solutions. We find that the wave approximation, which is of a conceptual nature, encapsulates quite faithfully the characteristics of the nonlinear Boussinesq equation solution and, overall, performs much better than the other methods, for which the relatively low performance can be attributed to the specific mathematical features of their construction. These endeavors might be useful for theoretical and modeling purposes related to this problem.