New developments in mathematical modeling of groundwater systems

Abdelkader Larabi
Senior Professor and Director of the Regional Water Centre of Maghreb, Mohammed V University, Rabat, Morocco

emails: larabi_abdelkader@yahoo.fr, larabi@emi.ac.ma

(2025) 78–80
https://doi.org/10.5004.dsal.2025.700104

Abstract

The numerical modeling of groundwater flow in unconfined aquifers is much more involved than in confined aquifers. This is because the governing equation (i.e., Richard’s equation) is highly nonlinear and is subject to nonlinear boundary conditions as well. This nonlinearity is related to the dependence of the relative permeability and the water retention in the unsaturated zone on the pressure head. Moreover, fully saturated models are typically associated with boundary conditions such as constant head, pumping/injection flow rates, and leakage flux through a semi‐confining bed. These are essentially linear and do not pose additional challenges to standard numerical solution techniques. This is not the case for unconfined flow models where some boundary conditions are nonlinear and therefore are unknowns a priori; thus, they are an integral part of the numerical solution. A typical example is the free and moving water table boundary. Another complication in modeling unconfined groundwater flow is to locate the position of seepage faces when the water table reaches the land surface. The seepage boundary faces are not known prior to the numerical solution and are, therefore, not fixed as typically done with other boundary conditions. Additionally, wells pumping groundwater from unconfined aquifers might become dry as the water table drops below the well screens, and natural or artificial drains may stop draining groundwater as the levels drop below predefined elevations. These are typical examples that necessitate additional bookkeeping procedures during the nonlinear iterative solution process when solving for an unconfined groundwater flow model. Furthermore, natural groundwater flow occurs mostly in highly heterogeneous and anisotropic materials, thus increasing the nonlinearity of the resulting discrete algebraic systems of the equations. Hence, robust and advanced numerical methods are needed in this context.

Keywords: Numerical modelling; Unconfined flow; Kinematic boundary condition; Water table position; Moving mesh; 3D mixed hybrid finite elements