Using Analytic Solution Methods on Unsaturated Seepage Flow Computations

This paper describes a change of variables applied to Richards’ equation for steady-state unsaturated seepage flow that makes the numerical representation of the new version of this highly nonlinear partial differential equation (PDE) much easier to solve, and the solution is significantly more accurate. The method is applied to two-dimensional unsaturated steady-state flow in a block of soil that is initially very dry until water is applied at the top. Both a quasi-linear version of relative hydraulic conductivity for which an analytic solution exists and a van Genuchten version of relative hydraulic conductivity are numerically solved using the original and new versions of the governing PDE. Finally, results of this research will be presented in this paper. It was found that for the test problem, the change-of-variables version of the governing PDE was significantly easier to solve and resulted in more accurate solutions than the original version of the PDE.