Numerical Solution of One Dimensional Unsaturated Water Flow Using A Reference-Operators Method

In this paper, a numerical solution is presented for one-dimensional unsaturated flows in the subsurface. Water flow in the subsurface, however, is highly nonlinear and in most cases, exact analytical solutions are impossible. The method of reference-operators has been used to formulate a discrete model of the continuum physical system. Many of the standard finite difference methods and also the finite volume method are special cases of the method of reference-operators. Unlike elementary finite difference methods, the method of reference-operators may by used to construct finite difference schemes on grids of arbitrary structure. A one-dimensional model was developed to predict the soil-water suction (negative pressure head) and water content in a vertical column of a layered soil. The model was verified against some available analytical solutions and experimental results and, in all cases, it showed good agreement.