By using toy, but non-trivial models for the water content and the hydraulic conductivity as functions of pressure, which describe transitions from unsaturated to saturated flow regime, we succeeded to verify explicit iterative schemes (described in a discussion started above) and to show their 2nd order convergence, for both one- and two-dimensional problems.
With the more realistic Genuchten-Mualem model, often used in applications, we have also shown the expected 2nd order convergence for a one-dimensional problem with manufactured solution using the parameters of a loam soil model picked up from the literature. Instead, the convergence test failed for a clay soil model, also often used in the literature.
The code verification and convergence tests for a similar two-dimensional problem failed for both soil models. It seems that the results are influenced by the dimensionality of the problem, as well as by the parameters of the soil model. The latter may, for instance, lead to “numerical singularities” consisting of divisions by very large numbers.
Any comments, suggestions, and examples of successful code verification tests using the van Genuchten-Mualem model are welcome.
Thank you
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