THREE-DIMENSIONAL FINITE ELEMENT MODELING OF GROUNDWATER FLOW (GALERKIN)

Scope and Method of Study. As over-development of surface waters depletes the water supply, the development and protection of groundwater is receiving more attention. The use of aquifiers as natural water storage facilities is becoming more common. Efficient use of aquifers as water storage facilities and greater dependence on groundwater to meet water demands require that effective tools be developed for groundwater management. Many large-scale groundwater aquifers are hydraulically connected through layers that may be semi-confining. Such coupling of aquifers definitely demands a simultaneous consideration of the entire system. A three-dimensional model provides the only convenient way of representing a field problem.;Findings and Conclusions. The finite element method is a reliable tool in solving the groundwater flow equation. The method eases the complexity of including the boundary and initial conditions in the system's equations. Making several runs and varying the sizes of the elements demonstrate that the degree of accuracy strongly depends on the size and therefore number of elements. Comparisons of model results with analytical and numerical solutions show excellent agreement.;A three-dimensional numerical model has been developed using Galerkin's finite element method. The model solves the partial differential equation of groundwater flow. The Gauss elimination procedure coupled with Cholesky's algorithm for banded matrices is used to solve the system of algebraic equations generated from the finite element approximation. The model is capable of simulating hydraulic head distributions in homogeneous/heterogeneous, isotropic/anisotropic, and leaky aquifers. Options for using two- or three-point Gauss numerical integrations are provided. The model can handle linear, quadratic, and cubic elements. It has been verified with existing one- and two-dimensional analytical solutions and a three-dimensional numerical model. The model was applied to the Ogallala aquifer in the Oklahoma Panhandle area.