CP-1994-11
On the numerical solutions of one-dimensional flow in the unsaturated zone.
El-Kadi, Aly I.
Analysis and prediction of water flow patterns in the unsaturated zone are critical to many water resources and environmental problems. Examples of such problems include infiltration, which is an important part of the hydrologic cycle encompassing the associated movement and storage of subsurface water. Soil properties are a major factor in controlling rainwater partition between infiltration and runoff as well as in controlling moisture movement. Hence, an accurate estimation of infiltration and the factors affecting it is required to facilitate a reliable prediction of runoff and subsurface moisture distribution. Another example is related to agricultural management in which unsaturated water flow needs to be considered in decision making regarding irrigation. Finally, chemical transport in the subsurface environment is greatly influenced, under certain conditions, by flow in the unsaturated zone. Contamination may be caused by leakage from sanitary landfills or by recharge of sewage water under unsaturated flow conditions. Irrigation and rainwater dissolve and carry fertilizers, pesticides, and other chemicals under unsaturated conditions also. In most cases, understanding chemical transport and transformations in the unsaturated zone is essential for assessing the actual or potential contamination of groundwater aquifers. Flow in the unsaturated zone is usually simulated by solving the Richards equation, which is derived by combining the mass conservation equation and Darcy’s law. Recent studies have reported problems in solving such an equation within a numerical framework. This paper reviews the theory and various conventional numerical solutions pertinent to the problem. It also covers recent advances in numerical techniques that are mostly aimed at improving the efficiency of the solutions by optimizing the size of the spatial and temporal increments. Most of the attempts are related, in general, to equation transformation, solution iteration, and interblock parameter estimation. However, there is still room for improvement, because in some cases accuracy may require the use of small increments, on the order of a few centimeters and seconds for the spatial and temporal increments, respectfully. Such a need is critical because of the burden involved in model applications for large-scale, multidimensional problems. Although only one-dimensional problems are addressed here, many of the issues involved can be readily extended to multidimensional cases.