Groundwater flow equation, overview, derivation, and solution

¹ Laboratories of mathematical and analysis, noncommutative geometry and applications, Faculty of Science, Ibn Tofail University, Campus Maamora, BP.133, 1400 Kénitra, Maroc.
² Laboratory of hydroinformatics, Faculty of Sciences, University Ibn Tofail, Campus Maamora, BP. 133 1400 Kenitra, Morocco.

Abstract

Darcy’s law is the basic law of flow, and it produces a partial differential equation is similar to the heat transfer equation when coupled with an equation of continuity that explains the conservation of fluid mass during flow through a porous media. This article, titled the groundwater flow equation, covers the derivation of the groundwater flow equations in both the steady and transient states. We look at some of the most common approaches and methods for developing analytical or numerical solutions. The flaws and limits of these solutions in reproducing the behavior of water flow on the aquifer are also discussed in the article.