MODFLOW-NWT: Newton Formulation

Written by Jakab András on .

The ï¬rst versions of the widely used groundwater flow model MODFLOW (McDonald and Harbaugh 1988) had a sure but inflexible way of handling unconï¬ned ï¬nite-difference aquifer cells where the water table dropped below the bottom of the cell—these "dry cells" were turned inactive for the remainder of the simulation. Problems with this formulation were easily seen, including the potential for inadvertent loss of simulated recharge in the model (Doherty 2001; Painter et al. 2008), and rippling of dry cells through the solution that unacceptably changed the groundwater flow system (Juckem et al. 2006).

Solving problems of the natural world often required the ability to reactivate dry cells when the water table rose above the cell bottom. This seemingly simple desire resulted in a two-decade attempt to include the simulation flexibility while avoiding numerical instability. Early attempts at "re-wetting" dry cells in MODFLOW, such as BCF2 were found to work for some, but not all, MODFLOW models. Re-wetting of dry cells was often numerically unstable and prevented model convergence, when BCF2 did have a stable solution, the resulting runtimes were appreciably longer, and BCF2 settings that worked in one model did not necessarily translate well to another.

After two decades of work, the general solution scheme used in MODFLOW was still simply not capable of robustly handling wet-dry problems. This realization led to a new approach to solving the equations used by MODFLOW, one using a Newton-Raphson solution rather than a Picard method. The Newton-Raphson formulation may be the single most important advancement to widely used ï¬nite-difference techniques since the release of the original MODFLOW.

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