Approximate Solution of Unsteady Groundwater Flows

Abstract

Kantorovich's method for obtaining approximate solutions to problems of unsteady diffusion of heat and momentum is applied to unsteady ground water seepage flow problems. Simple profiles satisfying free surface boundary conditions in the spatial domain are assumed, leaving the time dependence to be determined from the governing equations. The governing nonlinear partial differential equation is thus reduced to a nonlinear ordinary differential equation whose exact solution is easily obtained. Results obtained using second-order profiles for both the sudden buildup case and the sudden drawdown case compare well with experimental data.