Analytical solutions to the one‐dimensional nonlinear diffusion equation for flow through porous media
Allen F. Moench · Water Resources Research · 1973
The one‐dimensional nonlinear diffusion equation is solved approximately by an extension of the Neumann method for a step input to a semi‐infinite medium. The method of solution requires that the region under consideration be divided into an arbitrary number of zones, each zone having known constant diffusivities. The boundaries between zones move at rates that are initially unknown. Two problems are considered: (1) horizontal flow in an aquifer in which the transmissivity and storage coefficients are functions of hydraulic head and (2) horizontal absorption in an unsaturated soil for which the diffusivity is a function of moisture content. Computational results compare well with finite difference and other numerical solutions to the same problems. The technique has application to other nonlinear problems of the same type.