Transient groundwater flow between reservoirs and water-table aquifers

Abstract

Transient groundwater flow between a reservoir and a semi-infinite unconfined aquifer has been one of the fundamental research topics in hydrogeology. Prediction of water level changes in the aquifer, due to water level variations in the reservoir, is of importance in contamination control, irrigation and hydrology. The movement of groundwater under this condition is described by the nonlinear Boussinesq equation. Analytical solutions to this equation are limited to some special cases and often require tedious computations. In this study, a new solution technique is developed in which the Boltzmann transformation is used to reduce the Boussinesq equation to a nonlinear ordinary differential equation, and the water level distributions are calculated using the Newton-Raphson method. The solution procedure requires very little computational effort, and the solution has been verified by comparing with analytical and numerical solutions. This solution should have application in verifying other analytical or numerical solutions, and in many practical hydrogeological problems. Two linearized solutions are evaluated using the new analytical solution developed in this study. The linearized solution with respect to h 2 gives a better result than that linearized with respect to h.