a flexible numerical approach to solving a generalized Richards' equation problem and some applications

A numerical program has been developed to study the motion of a fluid (e.g. rainfall water) within a porous medium (e.g. soil) in unsaturated conditions; the motion was considered to be one- dimensional vertically downward in first approximation. The motion is governed by Richards’ Equation, which is integrated numerically by the program with a typical implicit finite-difference Crank-Nicholson scheme. The program can also integrate simultaneously the heat transport equation within the soil, with the same numerical scheme, which is generally suitable for parabolic problems. The problem is highly nonlinear because both equations’ coefficients (hydraulic and thermal conductivities, hydraulic and thermal capacities, etc) and source-sink terms can depend on the solution its elf, above all on the value of suction head. These dependencies are expressed by parametric relationships [Van Genuchten, Gardner, Brooks and Coorey, et al.] whose parameters are time-invariant but can be space-variant. The main goal of this work is to model the local behaviour of pressure head in space (at different soil depths) and time, with two purposes. The first one, which is strictly hydrological, is to estimate water volumes contained in soil and surface and subsurface fluxes in the vadose zones; the second one is the characterisation (by using an indefinite slope model) of the variations of hillslope safety factor due to the variations of water pressure head and soil effective stresses during severe rainfall events.