Three-dimensional local grid refinement for block-centered finite-difference groundwater models using iteratively coupled shared nodes: a new method of interpolation and analysis of errors

摘要

This paper describes work that extends to three dimensions the two-dimensional local-grid refinement method for block-centered finite-difference groundwater models of Mehl and Hill [Development and evaluation of a local grid refinement method for block-centered finite-difference groundwater models using shared nodes. Adv Water Resour 2002;25(5):497-511]. In this approach, the (parent) finite-difference grid is discretized more finely within a (child) sub-region. The grid refinement method sequentially solves each grid and uses specified flux (parent) and specified head (child) boundary conditions to couple the grids. Iteration achieves convergence between heads and fluxes of both grids. Of most concern is how to interpolate heads onto the boundary of the child grid such that the physics of the parent-grid flow is retained in three dimensions. We develop a new two-step, "cage-shell" interpolation method based on the solution of the flow equation on the boundary of the child between nodes shared with the parent grid. Error analysis using a test case indicates that the shared-node local grid refinement method with cage-shell boundary head interpolation is accurate and robust, and the resulting code is used to investigate three-dimensional local grid refinement of stream-aquifer interactions. Results reveal that (1) the parent and child grids interact to shift the true head and flux solution to a different solution where the heads and fluxes of both grids are in equilibrium, (2) the locally refined model provided a solution for both heads and fluxes in the region of the refinement that was more accurate than a model without refinement only if iterations are performed so that both heads and fluxes are in equilibrium, and (3) the accuracy of the coupling is limited by the parent-grid size—a coarse parent grid limits correct representation of the hydraulics in the feedback from the child grid.