On the construction of a functional solution method for the infiltration in porous media problems

In this paper, we consider a transient vertical one-dimensional flow problem of water in unsaturated porous media, modelled by the non-linear Richards equation. Constitutive relations of Van Genuchten will be employed and Padé approximants are used to represent the hydraulic capacity and conduction in a simplified fashion. From the proposed methodology a construction of a functional solution is presented with the objective to define an initialisation of a recursive scheme in the spirit of Adomian decomposition. This solution is optimised and evaluated using the governing equation for a self-consistency test. The results are presented for some soil types and its related soil parameters, that are reported in the literature.