New Analytical Solution to Water Content Simulation in Porous Media

AbstractThe nonlinear advection-diffusion equation, also known as Richard’s equation, is one of the most famous equations expressing water content in unsaturated porous media with broad applications in hydrology, engineering, and soil sciences. Because of the inherent nonlinearity in the equation, its closed-form analytical solution is rare. The traveling wave solution (TWS) is one of the recent exact approaches used in solving nonlinear partial differential equations (PDEs) and seems to be a suitable and efficient approach to obtain analytical solutions for Richard's equation. This paper presents three major cases of Richard’s equation that are tackled with the TWS method using general and modified forms of tanh⁡ function scheme to obtain the exact solution for each equation. The typical forms of diffusivity and conductivity functions proposed by Brooks and Corey are considered, and the exact solution for Richard’s equation is presented. Solutions have a broad applicability in pertinent engineering and s...