Modeling 3D Ground‐Water Flow by Modified Finite‐Element Method

Abstract

In this study, a number of theoretical improvements were made to the finite‐element formulation for modeling three‐dimensional steady and unsteady ground‐water flow. First, the Galerkin method was combined with the collocation method to handle the time‐derivative term of the governing equation. Second, the resulting system of ordinary differential equations was solved by using finite integration. The principal directions of the anisotropy are not required to parallel the user‐selected global coordinate directions. Also, more detailed treatments to leaky boundaries, surface flux boundaries, nonhomogeneous and anisotropic aquifers, and sources/sinks are presented. The improved formulation was coded in FORTRAN. Four example cases were used to verify the model. It was found that the model is stable, accurate, and numerically oscillation free if proper time‐step size is used. A critical review of the commonly used finite‐difference solution scheme is given. A detailed discussion of how to obtain accurate numerical solutions while avoiding numerical oscillation is presented.