Homotopy analysis of 1D unsteady, nonlinear groundwater flow through porous media

In this paper, the 1D unsteady, nonlinear groundwater flow through porous media, corresponding to flood in an aquifer between two reservoirs, is studied by mass conservation equation and Forchheimer equation instead of Darcy's law. The coupling nonlinear equations are solved by homotopy analysis method (HAM), an analytic, totally explicit mathematic method. The method uses a mapping technique to transfer the original nonlinear differential equations to a number of linear differential equations, which does not depend on any small parameters and is convenient to control the convergence region. Comparisons between the present HAM solution and the numerical results demonstrate the validity of the HAM solution. It is further revealed the strong nonlinear effects in the HAM solution at the transitional stage.