Numerical Solution of Boussinesq Equation

The Boussinesq equation is a mathematical model of unconfined ground-water flow. Since the equation is nonlinear, finite difference methods offer a possible technique for solutions. In this study, an extrapolated Crank-Nicolson finite difference scheme for one-dimensional Boussinesq equation with source and sink terms is described to model the flow through a phreatic aquifer lying between two open channels. Generalized traveling wave solutions of the same equation are also obtained. A comparison of the extrapolated Crank-Nicolson solution with a traveling wave solution confirms the accuracy of the former. Details of the response of an unconfined aquifer subject to different rates of recharge and withdrawal are presented.