Application of confined aquifer theory for verification of solutions of water flow towards a drain in saturated–unsaturated soil

The method for verification of numerical solution of water flow towards a drain in homogeneous soil under steady rainfall or steady irrigation recharge is presented in the paper. In 1979, Zaradny and Feddes proved that the accuracy of the numerical result depended, among other things, on the size and pattern of discretization applied. Ibidem, a partly verification of numerical solution was presented. It was based on the Thiem–Dupuit well formula and on the hodograph solutions given by Van Deemter [Van Deemter, J.J., 1950. Versl. Landb. Onderz. 56 (7), 1–67] and Childs [Childs, E.C., 1959. J. Soil Sci. 10 (1), 83–100]. Up till now, there was no full verification of this solution. The proposed method which depends on replacement of the drain by horizontal ‘well’ in a confined aquifer of a constant thickness, the geometry of which in the x–z plane is compatible, in shape and size, with saturated zone in the numerical solution gives the possibility of such verification. For this problem groundwater flow can be described by the Laplace equation. The analytical solutions for the hydraulic head φ and the stream function ψ, specification of boundary conditions for the considered problem and the method of determination of the Fourier series constants are given in the paper. Presented results confirm the correctness of numerical solution given by Zaradny and Feddes [Zaradny, H., Feddes, R., 1979. Agric. Water Manage. 2, 37–53] and they also show that when verification with respect to observed and measured data is impossible, such tests should be performed.