Approaches to the Simulation of Unconfined Flow and Perched Groundwater Flow in MODFLOW

Various approaches have been proposed to manage the nonlinearities associated with the unconfined flow equation and to simulate perched groundwater conditions using the MODFLOW family of codes. The approaches comprise a variety of numerical techniques to prevent dry cells from becoming inactive and to achieve a stable solution focused on formulations of the unconfined, partially-saturated, groundwater flow equation. Keeping dry cells active avoids a discontinuous head solution which in turn improves the effectiveness of parameter estimation software that relies on continuous derivatives. Most approaches implement an upstream weighting of intercell conductance and Newton-Raphson linearization to obtain robust convergence. In this study, several published approaches were implemented in a stepwise manner into MODFLOW for comparative analysis. First, a comparative analysis of the methods is presented using synthetic examples that create convergence issues or difficulty in handling perched conditions with the more common dry-cell simulation capabilities of MODFLOW. Next, a field-scale three-dimensional simulation is presented to examine the stability and performance of the discussed approaches in larger, practical, simulation settings.