A new ghost-node method for linking different models and initial investigations of heterogeneity and nonmatching grids

• Published in: Advances in water resources 2007-08, Vol.30 (8), p.1722-1736
• Main Authors: Dickinson, Jesse E., James, Scott C., Mehl, Steffen, Hill, Mary C., Leake, S.A., Zyvoloski, George A., Faunt, Claudia C., Eddebbarh, Al-Aziz
• Format: Article
• Language: English
• Subjects: aquifers; Earth sciences; Earth, ocean, space; Exact sciences and technology; FEHM; FEHM model; Finite-difference; Finite-element; ghost-node method; groundwater flow; Groundwater models; hydraulic conductivity; hydrogeology; hydrologic models; Hydrology. Hydrogeology; Interpolation; Local grid refinement; mathematical models; MODFLOW; MODFLOW model; simulation models
• ISSN: 0309-1708; 1872-9657
• DOI: 10.1016/j.advwatres.2007.01.004

A flexible, robust method for linking parent (regional-scale) and child (local-scale) grids of locally refined models that use different numerical methods is developed based on a new, iterative ghost-node method. Tests are presented for two-dimensional and three-dimensional pumped systems that are homogeneous or that have simple heterogeneity. The parent and child grids are simulated using the block-centered finite-difference MODFLOW and control-volume finite-element FEHM models, respectively. The models are solved iteratively through head-dependent (child model) and specified-flow (parent model) boundary conditions. Boundary conditions for models with nonmatching grids or zones of different hydraulic conductivity are derived and tested against heads and flows from analytical or globally-refined models. Results indicate that for homogeneous two- and three-dimensional models with matched grids (integer number of child cells per parent cell), the new method is nearly as accurate as the coupling of two MODFLOW models using the shared-node method and, surprisingly, errors are slightly lower for nonmatching grids (noninteger number of child cells per parent cell). For heterogeneous three-dimensional systems, this paper compares two methods for each of the two sets of boundary conditions: external heads at head-dependent boundary conditions for the child model are calculated using bilinear interpolation or a Darcy-weighted interpolation; specified-flow boundary conditions for the parent model are calculated using model-grid or hydrogeologic-unit hydraulic conductivities. Results suggest that significantly more accurate heads and flows are produced when both Darcy-weighted interpolation and hydrogeologic-unit hydraulic conductivities are used, while the other methods produce larger errors at the boundary between the regional and local models. The tests suggest that, if posed correctly, the ghost-node method performs well. Additional testing is needed for highly heterogeneous systems.