Numerical Simulation of Two-Dimensional Unsaturated Flow from a Trickle Irrigation Source Using the Finite-Volume Method

Abstract

A numerical two-dimensional finite-volume model is developed to predict the moisture-based form of the Richard’s equation that describes the transient flow of water through homogeneous and heterogeneous unsaturated porous media from a trickle irrigation source in a cylindrical flow region. Clay loam soil is selected to represent the homogeneous porous media. This cylindrical flow domain of clay loam soil is initially at uniform volumetric water content. Numerical runs were conducted with a clay loam soil at water application rates from the trickle irrigation source at a small circular pond area. An assessment of the fully implicit and explicit time schemes and arithmetic and geometric mean weighing formulas are evaluated. A good agreement is obtained when comparing the experimental measured positions of the wetting front advance with the predicted results. In general, for numerical modeling of the unsaturated flow equation, the fully implicit time scheme with geometric mean weighing formula for estimating the approximate value of the nonlinear soil water diffusivity and hydraulic conductivity at the interface between adjacent control volumes can be recommended when the theta-based form of the Richard’s equation is solved. The predicted results show that the finite-volume method is mass conservative, and it is a recommended method for solving Richard’s equation.