Infiltration from Trickle Irrigation Source

Abstract

The two-dimensional nonlinear partial differential equation that describes the transient movement of water in an unsaturated porous medium is investigated by using the zero-order continuous linear finite element method. The governing equation is transformed logarithmically to smooth the abrupt changes in the soil-water characteristic relations. The Newton-Raphson method is used to iterate toward the "exact" solution of the original nonlinear equations. In addition, a modified implicit finite difference scheme is used to approximate the time derivatives. Predictions of the finite element model are verified with a one-dimensional example. The model is then used to investigate two-dimensional infiltration from a trickle irrigation source. The numerical results compare well with those obtained from laboratory and field experiments. The advantage of the present model is its capability to simulate water movement through very dry soil environments, which causes a steep moisture front, as well as its potential applicability in irregularly shaped flow regions, which are commonly encountered in the field and are difficult to model with finite difference or other numerical methods.