Extension of the Dupuit–Forchheimer Model for Non-Hydrostatic Flows in Unconfined Aquifers

Abstract

The classical Dupuit–Forchheimer approach, commonly used in analysing unconfined groundwater-flow systems, relies on the assumption of a negligible vertical component of the flow. This approximation is valid only when the convergence of streamlines is very limited and the drawdown of the phreatic surface is small, or the thickness of the horizontal layer of the heterogeneous aquifers is sufficiently small. In this study, a higher-order one-dimensional model is proposed for groundwater-flow problems with significant inclination and curvature of the phreatic surface. The model incorporates non-hydrostatic terms that take into account the effects of the vertical velocity of the flow, and was solved with an implicit finite-difference scheme. The accuracy of the proposed model was demonstrated by simulating various unconfined seepage- and groundwater-flow problems with moderate curvilinear effects. The computational results for steady-state flows were compared with the results of the full two-dimensional potential-flow methods and experimental data, resulting in a reasonably good agreement. In general, the comparison results exhibited the efficiency and validity of the model in simulating complex unconfined flows over curved bedrock and curvilinear flows over planar bedrock with a steep slope.

Keywords

• groundwater hydrodynamics
• unconfined flow problems
• porous media
• seepage surface
• hillslope hydrology
• free-boundary problems