Approximate Solutions for Horizontal Unconfined Aquifers in the Buildup Phase

Elias Gravanis, Evangelos Akylas, Ernestos Nikolas Sarris

    Research output: Contribution to journalArticlepeer-review

    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.

    Original languageEnglish
    Article number1031
    JournalWater (Switzerland)
    Volume16
    Issue number7
    DOIs
    Publication statusPublished - Apr 2024

    Keywords

    • analytical solutions
    • approximate solutions
    • buildup phase
    • early times
    • self-similar solutions
    • unconfined aquifer
    • wave

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