Approximate analytical solution of the nonlinear diffusion equation for arbitrary boundary conditions
A general approximation for the solution of the one- dimensional nonlinear diffusion equation is presented. It applies to arbitrary soil properties and boundary conditions. The approximation becomes more accurate when the soil-water diffusivity approaches a delta function, yet the result is still very accurate for constant diffusivity suggesting that the present formulation is a reliable one. Three examples are given where the method is applied, for a constant water content at the surface, when a saturated zone exists and for a time-dependent surface flux.
Record created on 2005-12-09, modified on 2016-08-08