A few topics for a challenging Master thesis

It is quite a long time that I am thinking to assign some master thesis around GEOtop 3.0.

A Master Thesis could be done even on the "simple" Richards equation. In this case the idea would be implementing the nested-Newton Casulli-Zanolli's method (on unstructured grids).

Time ago I assigned a little grant on this topic, but unfortunately, the work was not completed/ The material produced, in any case, is here. (I have also some other material, in FORTRAN, anyway).  In this case, the idea would be to use Java and develop further what already made by Francesco Serafin in his thesis. 

My outstanding colleague Michael Dumbser already promised to help me to complete the precedent work, and, at that point the main work would be to translate the procedural concepts into a object-oriented framework. In any case, who does it, would place one of the first stones of GEOtop 3.0.

Just thinking loudly, once started the Richards' work (which constitutes, however,  well defined and challenging enterprise) one could think how to implement coherently different flavours of the equation, for using bimodal or other water retention curves; for extending Richards analysis to integrate also the groundwater 3D equation, or studying the coupling with the evaporation/transpiration sink.  All alternatives that are interesting either from the numerical and the physical point of view.

The original problem I had in mind when I started this post, was the more ambitious one connected with the numerics and the physics of soil freezing (see Matteo Dall'Amico Ph.D. Thesis).  Our reference paper in the topic is the 2011 Dall'Amico et al. In the thesis and in the paper we wrote the equations in  3D but solved them in 1D with a not so particularly elegant method, which the nested-Newton algorithm could surpass by far. 

Working on the cryospheric side of Richards equation open a series of opportunity and especially the collaboration with  Stephan Gruber (with Carleton we have an exchange agreement, and the candidate could also stay for a few months there). 

Actually all these topics suggest that a very basic trial could be made to envision a scheme and an infrastructure that can accomodate all of these Richards variants by minimising code rewriting. But this would be probably a theme that could be completely developed in a Ph.D. In fact all these topics' task can clearly produce journal papers, if completed, and certainly open the road to some Ph.D. carrier.

Someone can think that everything is too much challenging, and actually, it is. However, all the topics are pretty mature in my mind, and the path to the solution is pretty well designed.