Approximate Solutions of the Boussinesq Equation for Horizontal Unconfined Aquifers During Pure Drainage Phase

Abstract

In this work, conceptual approximations of the Boussinesq equation were introduced and analyzed, resulting into a very accurate and well-applicable model for horizontal unconfined aquifers during the pure drainage phase, without any recharge and zero-inflow conditions. The model was constructed by employing a variety of methods that included wave solution, variable separation, and series expansion, and its analysis and performance against the Boussinesq equation, at early and later times, providing fruitful insights enlightening the main mechanisms and physical characteristics of the drainage phase. The modeled non-linear forms were finally linearized, concluding with explicit analytical expressions that accurately incorporated most of the basic characteristics regarding the evolution of the water table and the outflow from the exact Boussinesq equation under different initial conditions. The endeavors of this work can be utilized for theoretical and modeling purposes related to this problem.