An integral transform method for the linearized Boussinesq Groundwater Flow Equation

Abstract

An analytical procedure is developed for the determination of potentiometric head in nonhomogeneous aquifers. Both steady and unsteady flow conditions are considered. The analytical procedure is based upon the use of orthogonal functions. It consists essentially of assuming an appropriate orthogonal series for both the aquifer properties and the unknown potentiometric head. The technique is applied to several one‐ and two‐dimensional flow problems where conditions are described by the linearized Boussinesq equation. The result of the analysis is the expression of potentiometric heads in analytic form. Subsequent use of Darcy's law yields accurate, analytic equations for the associated velocity fields. Such representations of the flow field are a potential benefit for prediction of mass transport in groundwater since velocity is known as a continuous function of space and time. Other useful features of the orthogonal series approach include its straightforward application. The approach is also shown to eliminate the introduction of discretization errors associated with the use of node systems which are required by many alternative numerical methods.