A mass-conservative method for the integration of the two-dimensional groundwater (Boussinesq) equation

This work presents with a new conservative finite-volume numerical solution for the two-dimensional groundwater flow (Boussinesq) equation, which can be used for investigations of hillslope subsurface flow processes and simulations of catchment hydrology. The Boussinesq Equation is integrated for each grid element and can take account of the local variability of topography and soil properties within the grid elements. The numerical method allows for wetting and drying of the water-table, which has been successfully simulated. The stability and convergence of the method is shown to be guaranteed \textit{a priori} by the properties of the solver itself. The numerics are validated against some approximate analytical solutions, and compared to another numerical solver of the Boussinesq equation. Finally, the solver capabilities are further explored with simulations of the Panola experimental hillslope where the bedrock topography, which is accurately known, causes complex wetting and drying patterns; in this situation the importance of a two-dimensional description of subsurface flows to obtain properly simulated discharges becomes clear.