The work carried out by Eligio Colmenares was distinguished by the UdeC Graduate School
The Graduate School of Universidad de Concepción conducted for the first time, the Doctoral Thesis Contest with the objective of recognizing and rewarding doctoral theses that have high levels of excellence and constitute a contribution of knowledge to the development of sciences, technologies and humanities in our country. In this context, the thesis Mixed Finite Element Methods for the Stationary Boussinesq Model was awarded in Applied Sciences and Technology category- which brings together applicants from many Doctorate programs such as Energy, Computing, Electrical Engineering and Forestry Engineering, among others. This work developed by Eligio Colmenares under the direction of Gabriel Gatica, director of the Center for Research in Mathematical Engineering, CI²MA, and Ricardo Oyarzúa, external associate researcher of this center and academician of the Department of Mathematics of the Faculty of Sciences of the Universidad del Bío-Bío.
In his research work, Colmenares addressed the stationary Boussinesq problem, which is given by a system of partial differential equations constituted by the Navier-Stokes and the diffusion-advection equations, non-linearly coupled through forces of buoyancy and heat transfer by convection. Regarding the applications of the developed model, Colmenares explains that “our goal was to provide numerical techniques to describe and quantify not only the main variables inherent to such phenomenon, such as the speed, pressure and temperature of the fluid, but also other variables of physical interest such as the pseudo-stress tensor, the vorticity, and the velocity and temperature gradients. We demonstrate theoretically why these techniques worked, under what conditions, with what precision they did it; and we verify it through numerical simulations in two and three spatial dimensions. In addition, we built adaptive algorithms to strengthen the robustness of the techniques making them more reliable and efficient computationally”. It must be noted that five articles already published in internationally renowned journals in the area of Numerical Analysis arose from this thesis. In turn, several extensions of Eligio's work is currently generating various topics for new undergraduate and postgraduate theses.
Regarding the recognition granted by the Graduate School, Colmenares explains that “I am deeply proud because the contest not only involves all the other Doctoral programs of the UdeC, but also requires that the thesis effectively constitute a contribution of knowledge to the development of sciences, technologies and humanities in the country. I am very grateful because, in a certain way, all the effort, dedication and even the suffering that we all go through when we develop a PhD thesis are recognized, which is an extremely enriching experience, but also very demanding personally and intellectually. It is always motivating to receive this kind of recognition because, in addition to giving merit to the work that we do, in a certain way, the discipline we are dedicated to, is also awarded and the dedication which we do it”.
For Eligio, the preparation received in our Center during his Doctorate studies was essential to obtain this award “In the first place, studying within the CI²MA allowed me to train with professors from the Universidad de Concepción who are very demanding, willing and brilliant, with a high level of scientific productivity and who are nationally and internationally recognized. This is, in fact, the reason why I chose to study this Doctorate program. In addition, one is there immersed in an environment where research is constantly perceived through their own classes, lectures, seminars, publications and even through interaction with other researchers, including from other countries, who visit the Research Center throughout the year and that having the chance to meet them. All these aspects I believe directly and indirectly influenced this achievement and are key not only in the successful development of a thesis but also in the formation of any future researcher”, he states and highlights that “this award is also, without a doubt, a recognition to my tutors Gabriel Gatica and Ricardo Oyarzúa for their invaluable support during the development of my Doctorate and for assuming the direction of my thesis with responsibility and seriousness”.