An Analytic Solution of Water Transport in Unsaturated Porous Media

One of the most well-known equations to describe the behavior of the infiltration of unsaturated zones in soil as a porous medium is known as Richards' equation. Although analytical approaches in simulating infiltration are few, there are many numerical researches to model this physical phenomenon. The Adomian decomposition method (ADM) is one of the most recent approaches used in solving nonlinear partial differential or algebraic equations, and is an easy way to achieve the analytic solution. In this article, two refined approaches in improving ADM are used to simulate volumetric water content via Richards' equation. The first modification was recently presented by Wazwaz using a new regrouping approach in Adomian series terms and the last is the Pade approximation. A comparison of the exact solution and (modified) ADM illustrate very good coverage and results.