Approximate Analytical Solution of the Nonlinear Diffusion Equation for Arbitrary Boundary Conditions

ISSN:
1573-1634
Keywords:
nonlinear diffusion ; analytic solutions ; exact solutions ; approximations ; similarity
Source:
Springer Online Journal Archives 1860-2000
Topics:
Geosciences
Technology
Notes:
Abstract 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.
Type of Medium:
Electronic Resource
URL: