Analytical solutions of groundwater flow have been reported for idealized groundwater systems; however, a more common approach to solving the distributed-para-meter, time-dependent partial differential equations that govern the groundwater flow is through numerical techniques such as the finite-difference or finite-element methods. These techniques transform the partial differential equations into a system of algebraic equations. The solution of the system of algebraic equations determines the head values at a predetermined set of discrete nodal points within the aquifer system.
Finite-difference approximation is based on the Taylor series representation of the time and spatial derivatives. It is conceptually more straightforward than the finite-element approximation and easy to implement. Finite-element approximation is based on the method of weighted residuals. For many groundwater problems, the finite-element method may be more advantageous over the finite difference-method. Medium heterogeneity and irregular boundary conditions are handled easily by the finite element method. This contrasts with finite-difference approximation that requires complicated interpolation schemes to approximate complex boundary conditions. Moreover, in the finite-element method, the size of the elements can easily be varied to reflect rapidly changing state variables or parameter values. The piecewise continuous representation of the dependent variables and, possibly, the parameters of the groundwater system can also increase the accuracy of numerical approximation (Willis and Yeh, 1987).
Since these two types of numerical methods have been applied to many fields, references are abundant in the literature. Willis and Yeh (1987), Anderson and Woessner (1992), and Sun (1994b) have provided detailed analyses of how these two methods are to be applied to groundwater modeling. It is also worth noting that many established groundwater modeling softwares are available in the public domain. Bedient et al. (1994) provided a summary listing of existing numerical models of groundwater flow and solute transport.
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