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- Luciano Gajardo and Estefanía Olivares were supervised by Dr. Manuel Solano, a researcher at CI²MA at the Universidad de Concepción and CMM at the Universidad de Chile.
Contributing to the understanding of the physical phenomena that occur in the process of water desalination through membranes was the central objective of the Ring Project “Computational Mathematics for Desalination Processes,” DSALT, (ACT210087) of the National Research and Development Agency.
In pursuit of this objective, Luciano Gajardo Chamblás and Estefanía Olivares Zamora presented their findings as part of their thesis for a degree in Mathematical Civil Engineering from the Universidad de Concepción (UdeC).
In Luciano’s case, his thesis, “An HDG method for a transport equation with non-linear boundary conditions,” was supervised by Manuel Solano Palma, an academic at the Universidad de Concepción (UdeC) and researcher at the Center for Mathematical Modeling (CMM) at the Universidad de Chile.
This work addressed “the proposal and analysis of an HDG (Hybrid Discontinuous Galerkin) scheme for a convection-diffusion equation with nonlinear boundary conditions,” explained Luciano, adding that the study aimed to improve understanding of numerical methods for simulations in “reverse osmosis desalination processes, studying in particular only the salt concentration equation, with the given velocity and a nonlinear boundary condition that tells us how salt adheres to the channel membranes.”
This is where the novelty of this research lies. “It was demonstrated that the continuous and discrete problems are well posed (under certain conditions), and that the HDG scheme was successfully implemented computationally, verifying the theoretical results obtained and making it possible to apply it to the case of interest, which is the desalination process,” Luciano explains.
The civil engineer and mathematician from the UdeC is beginning his doctoral studies in Applied Mathematics at Simon Fraser University (Canada). “My plans are to devote myself to research in the academic world in applied mathematics, starting with this doctorate. I also love university teaching, so I hope to be able to combine both.”
Estefanía, meanwhile, developed her thesis, “A conservative HDG method for the coupled Navier-Stokes and Advection-Diffusion equations,” under the supervision of Sander Rhebergen of the University of Waterloo (Canada) and Professor Solano himself. In it, the now engineer “focused on doing an a priori analysis of the coupled problem of the Navier-Stokes equation with Advection-Diffusion, having nonlinear conditions in what we call the domain membrane,” she explains, noting that “we managed to do an a priori error analysis under some hypotheses that could be relaxed in future work.”
As for her immediate future, Estefanía says, “I am interested in continuing my research. At the moment, I am analyzing my options so I can decide where to continue my research.”
Both Estefanía and Luciano had international experiences—at Waterloo SFU, respectively—while still completing their final semesters of undergraduate studies, which had a positive impact on their interest in pursuing careers in science.
“The international stay helped me learn new methods and software to implement the results. It was an enriching experience that also showed me what academia is like in other countries,” says Estefanía.
Meanwhile, Luciano emphasizes that “the stay was an interesting process that opened doors, provided contacts, and was a good experience both personally and academically.”
Prof. Solano, also a member of the Center for Research in Mathematical Engineering (CI²MA) at the UdeC, noted that “Estefanía and Luciano addressed the same problem that models the reverse osmosis process in desalination channels, but with a different numerical approach. Estefanía studied a conservative primal HDG method, and Luciano did the same with a mixed formulation HDG method. They did an excellent job, and I hope they are encouraged to continue their postgraduate studies.”
By Iván R. Tobar Bocaz, CMM Communications
Posted on Sep 16, 2025 in News
