[1] This technical note derives clean analytical solutions of Richards' equation for threedimensional unsaturated groundwater flow. Clean means that the boundary conditions and steady state solutions are closed form expressions and the transient solutions have relatively simple additional Fourier series terms. Two-dimensional versions of these solutions are also given. The primary purpose for the solutions is to test linear and nonlinear solvers in finite difference/volume/element computer programs for accuracy and scalability using architectures ranging from PCs to parallel high-performance computers. This derivation starts from the quasi-linear assumption of relative hydraulic conductivity varying exponentially with pressure head and the separate approximation that relative hydraulic conductivity varies linearly with moisture content. This allows a transformation to be used to create a linear partial differential equation. Separation of variables and Fourier series are then used to obtain the final solution. Physically reasonable material properties are also used. A total of four solutions are given in this technical note (steady state and transient solutions for two different boundary conditions of the sample problem).
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.