Subsurface-Surface Water Flow and the Nested Newton Algorithm by Vincenzo Casulli

 On March 19th we had in Trento Martyn Clark (GS), Louise Arnal (GS) and Wouter Knoben (GS) to discuss about common research pathways. It was a dense day of discussions and exchange of ideas that started from the Mesiano terrace, continue inside, at the pizzeria Korallo, and later with an aperitif in Piazza Fiera and could have continued for days. You realize that the afternoon is missing. The afternoon was even better because Vincenzo Casulli (GS) gave a couple of talks about how to integrate subsurface and surface flow, and about his Nested Newton algorithm for solving a special class of non linear problems. Vincenzo agreed to record his talks and now you can appreciate them here below.  

Three papers that affected my recent research

Stimulated by the quarantine and by chain letters regarding books or movies, by my FB friends, I tried to think to a similar chain for papers inviting research friends to expose five paper among those that they were important in recent years. My own five were:

• 1/5 - Rodriguez-Iturbe, I., and J. B. Valdes. 12/1979. “The Geomorphologic Structure of the Hydrologic Response.” Water Resources Research 15 (6): 1409–20.
• 2/5 - Freeze, R. A., & Harlan, R. L. (1969). Blueprint for a physically-based, digitally-simulated hydrologic response model. Journal of Hydrology, 9(3), 237–258. doi:10.1016/0022-1694(69)90020-1

But these go back quite in time and affected almost all of my research. So they do not count for the title. They are very recognized benchmark papers. Important for anyone.

The three are recent:

• 3/5 Botter, Gianluca, Enrico Bertuzzo, and Andrea Rinaldo. 2010. “Transport in the Hydrologic Response: Travel Time Distributions, Soil Moisture Dynamics, and the Old Water Paradox.” Water Resources Research 46 (3). http://doi.wiley.com/10.1029/2009WR008371.
• 4/5 Casulli, Vincenzo, and Zanolli, Paola. 2010. “A Nested Newton-Type Algorithm for Finite Colume Methods Solving Richards’ Equation in Mixed Form.” SIAM Journal of Scientific Computing 32 (4): 2225–73.
• 5/5 Schymanski, Stanislaus J., and Dani Or. 2017. “Leaf-Scale Experiments Reveal an Important Omission in the Penman–Monteith Equation.” Hydrology and Earth System Sciences 21 (2): 685–706.

As in the tradition of these chains,  no explanations but the links to the papers, yes

Freezing-thawing processes studying with numerical models

This is the presentation given by Niccolò Tubini at the Carleton University last October 6th. Niccolò in his Master Thesis is working for a new implementation of the theory of freezing and thawing already covered by Matteo Dall'Amico in his Ph.D. Thesis and in Dall'Amico et al., 2011.

This work is part of the GEOtop project and its new implementations (see also here). The intention is to use the new numerical method implemented by Casulli and Zanolli (2010, 2011) of the extended Richards equation (see also the video here). The new method promise to be faster than the older one, more stable, and implemented for unstructured grids, while at present, GEOtop 2.0 uses a structured grid. Hopefully, the new development will be made in OMS3. 

References

Casulli, V., & Zanolli, P (2010). A nested newton-type algorithm for finite colume methods solving Richards' equation in mixed form. SIAM J. SCI. Comput., 32(4), 2225–2273.

Casulli, V., & Zanolli, P. (2012). Iterative solutions of mildly non linear systems, Journal of Computational and Applied Mathematics, 236(16), 3937–3947. http://doi.org/10.1016/j.cam.2012.02.042

Dall'Amico, M., Endrizzi, S., Gruber, S., & Rigon, R. (2011). A robust and energy-conserving model of freezing variably-saturated soil. The Cryosphere, 469–484. http://doi.org/10.5194/tc-5-469-2011

A solver for the 1D de Saint-Venant equation in OMS

A simplified but not so simplified way to describe the motion in channels, is to use the de Saint Venant 1d equation. Solving it is not anymore a particularly complex model and almost twenty years ago, I and collaborators implemented one of it based on Vincenzo Casulli work.  This can be seen, from Angelo Zacchia's master thesis (in Italian), which contains the main elements from page 36 to 51. A more scientific treatment of the problem is presented in Casulli and Zanolli [1998], and Aldrighetti's Ph. Thesis [2007].

This work is simpler but implemented inside the JGrasstools, by Silvia Franceschi (of Hydrologis) during her Google Summer of Code 2015 exercise,  and available as open source here.
A little of documentation is in the GSoC 2015 page of the project itself.

References

Aldrighetti, E., Computational hydraulic techniques for theSaint Venant Equations in arbitrarilyshaped geometry, 2007

V. Casulli and P. Zanolli. A conservative semi-implicit scheme for open channel flows. International Journal of Applied Science & Computations, 5:1–10, 1998.

Zacchia,  A., Master Thesis, Su alcuni metodi per la prevenzione e previsione del rischio idraulico, Trento University, 1997