The approximate analytical method for groundwater modelling

The approximate analytical method described in this report is a combined analytical and numerical analysis method for obtaining an approximate solution to a groundwater model which usually consists of partial differential equation(s). The attractive feature of this method is the resultant reduction in the dimensionality of the differential equation which is known to govern the flow of groundwater of the problem considered. The report offers a general formulation of the method based on related finite difference and finite element techniques. The finite difference formulation is a combination of the method of lines and an analytical solution; in the finite element formulation linear interpolation polynomials are used to convert the partial differential equations into a system of coupled ordinary differential equations which in turn is decomposed by an orthogonal transformation. The resultant equations are integrated by a suitable analytical method. The result of the equation integration is an analytical relationship. The method is illustrated by application to the equations governing two-dimensional steady state groundwater flow, one-dimensional and two-dimensional contaminant transport. For the groundwater flow problem, the accuracy of the approximate solution is examined by comparison with finite element modelling. The results of the two methods are virtually identical. For a time-dependent problem, a major saving in computational cost can be realized immediately, because the approximate analytical method leads to a closed-form solution for the time variable and, therefore, a time-marching scheme is not required. 16 refs