Evaluation of a local grid refinement method for steady-state block-centered finite-difference groundwater models

A new method of local grid refinement for two-dimensional block-centered finite difference meshes that uses an iteration-based feedback to couple two separate grids has been developed. Its convergence properties have been evaluated and comparisons with alternative methods have been completed (Mehl and Hill, in review a). This work further investigates a difficulty encountered with the traditional telescopic mesh refinement (TMR) methods that lack a feedback. Results indicate: (1) Coupling the coarse grid with the refined grid in a numerically rigorous way that allows for a feedback can improve the coarse grid results; this improvement is not possible using the TMR methods because there is no feedback. (2) The TMR methods work well in situations where the better resolution of the locally refined grid has little influence on the overall flow-system dynamics, but if this is not true, lack of a feedback mechanism produced errors in head up to 6.8% and errors in cell-to-cell fluxes up to 7.1% for the case presented. (3) For the TMR methods, coupling using flux boundary conditions produces significant inconsistencies in the head distribution at the boundary interface. TMR inaccuracies can substantially effect parameter estimation (Mehl and Hill, in review b).