A Numerical Investigation of Transient Groundwater Flows with a Phreatic Surface Along Complex Hillslopes

Most of the existing models for analyzing unconfined flows in hillslope aquifers are based on the Boussinesq (1877) equation. In the development of these models, the assumption of negligible bed-normal velocity was employed, thus restricting their application to shallow groundwater-flow situations. On the basis of a non-hydrostatic pressure approach, a ground-water-flow model that considers the effects of the vertical curvature of the flow streamlines and the three-dimensional geometry of the underlying bedrock was proposed. A dissipative two-four finite-difference scheme was utilized to discretize and solve the model equation. The applicability of the model was assessed by conducting numerical experiments on transient unconfined flows in convergent- and divergent-type hillslope aquifers with non-uniform bedrock slopes. The numerical results for the phreatic-surface profiles and outflow discharges were compared to the experimental data, and a good agreement was obtained. The results of the comparison attested that the dynamics of the hillslope drainage processes were accurately portrayed by the proposed model. This study highlights the necessity of considering the effects of the plan shape and the profile curvature of complex hillslopes in order to improve the overall performance of the computational model.