Transient Flow in Unsaturated Porous Media

Transient water movement in both horizontal and vertical unsaturated porous media is investigated. The nonlinear partial differential equation governing the one-dimensional flow is solved by the orthogonal collocation method. This method involves the approximation of the spatial derivative terms in the partial differential equation by an orthogonal polynomial and thus the partial differential equation is transformed into a set of ordinary differential equations which in turn can be integrated numerically. The present numerical solutions are found to be in excellent agreement with previous solutions for the cases under consideration. Because of its high accuracy, computational stability and easy implementation, the orthogonal collocation method can be a very good alternative for tackling these nonlinear diffusion problems.