Modelling subsurface water flow in the unsaturated zone - Mutandanyi, Tshanduko (University of the Free State, 2019)
Modelling flow in the unsaturated zone has caught interest recently in many fields of science such as geohydrology; agriculture; and soil physics. Unsaturated zone flow has a significant effect on the quality and quantity of groundwater resources; thus, it is essential to understand it. This thesis aimed to model water flow in the unsaturated zone. There are many studies in literature that aimed at understanding flow in this zone by means of mathematical models. Richards’ equation is commonly used in such studies and its performance has shown great success in reproducing the unsaturated flow system. However, complexities in the unsaturated zone and soil hydraulic properties make Richards’ equation to be highly non-linear which makes it impossible to solve analytically. As a result, it is mostly solved numerically using computer codes to obtain numerical solutions. However, linearized Richards’ equation can be solved analytically and reliable results can be obtained. The methodological approach of this thesis entails application of Brooks & Corey and Mualem non-linear hydraulic conductivity models to Richards’ equation. The resultant models were solved numerically and numerical solutions were obtained. Following that a linearized Richards’ equation was proposed and solved to obtain an exact solution. An exact solution was obtained using Laplace and inverse Laplace transform and Green’s function. For numerical analysis, both models were discretized using Crank-Nicolson and the Laplace Adam-Bashforth numerical approximation methods. The stability analysis was provided for the linear model for both methods. From the stability analysis, it was found that both numerical approximation methods yield stable solutions provided the required conditions are met. For the considered unsaturated flow system, it is concluded that the proposed linear model showed good performance in expressing water flow. Models proposed by Brooks & Corey and Mualem seemed to overestimate hydraulic conductivity resulting in an overestimation of soil moisture. These models were revised and the resultant models were able to yield results that correspond to results obtained using the proposed linear model.
Dissertation (M.Sc. (Institute for Groundwater Studies))--University of the Free State, 2019
Keywords: Unsaturated zone; Unsaturated flow system; Unsaturated hydraulic conductivity; Non-linear model; Richards' equation; Exact solution; Numerical simulations