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Simulation of contaminant transport in three dimensions: 1. The alternating direction Galerkin Technique
Author(s) -
Burnett R. D.,
Frind E. O.
Publication year - 1987
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr023i004p00683
Subject(s) - curvilinear coordinates , finite element method , finite difference , galerkin method , dispersion (optics) , finite difference method , flow (mathematics) , advection , representation (politics) , computer science , mathematics , mathematical optimization , geometry , mathematical analysis , engineering , physics , structural engineering , optics , politics , political science , law , thermodynamics
The alternating direction Galerkin technique for the simulation of advective‐dispersive transport in three dimensions is developed. The technique is designed for high efficiency in handling the large and detailed grids that are often required in simulations of natural groundwater systems. It is comparable to an alternating direction finite difference scheme, except for two advantages: first, the capability to handle certain curvilinear grids that may conform to either a flow net geometry or a natural stratigraphy and, second, the option to enhance solution accuracy through a choice between a finite difference or a finite element representation of the time derivative. Criteria for controlling numerical dispersion and accuracy can be applied easily. Three options for the time‐stepping algorithm are developed and analyzed for stability, and their accuracy is investigated for simple flow systems. The technique is shown to be far more efficient than a conventional three‐dimensional finite element model. In a companion paper, an application to a field‐scale contaminant transport problem is described.