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Sergio Caucao and Marco Discacciati collaborate in the study of equation coupling for modeling the behavior of fluids in heterogeneous porous media.
Dr. Sergio Caucao Paillán, a researcher at the Center for Mathematical Modeling (CMM) of the University of Chile, spent a research stay at Loughborough University (Leicestershire, United Kingdom) from Tuesday, November 5 to Friday, November 15.
The also academic of the Department of Applied Mathematics and Physics of the Faculty of Engineering of the Universidad Católica de la Santísima Concepción (UCSC) has been collaborating for about eight years with his peer of the Department of Mathematical Sciences of Loughborough University, Marcos Discacciati and currently, they are studying, explains Caucao, “the coupling of the Brinkman-Forchheimer and Darcy equations to model the behavior of an incompressible fluid passing through a heterogeneous porous medium. More precisely, an overlap-free domain decomposition method for the coupled Brinkman-Forchheimer/Darcy problem.”
“This work,” Dr. Caucao added, ”is also one of the objectives proposed in the recent group project awarded by the Research Group in Numerical Analysis and Scientific Calculus (GIANuC2) of UCSC. This project is financed by the UCSC Research Direction through the Internal Fund to Strengthen Research and Innovation Groups 2024”.
In addition to both researchers, Discacciati’s postdoctoral researcher, Dr. Nahuel Caruso, participates in this work. “I have known Marco since 2016”, Caucao explains, “when I did a research stay for two months at Loughborough University, in the context of my PhD at UdeC that I carried out under the supervision of professors Gabriel Gatica and Ricardo Oyarzúa. In that instance we worked on the coupling of the Navier-Stokes and Darcy-Forchheimer equations” and he adds that, as a result of that stay, an article was published in ESAIM: Mathematical Modelling and Numerical Analysis, co-written by Gatica, Oyarzúa, Discacciati and himself.
In 2022, meanwhile, Caucao again contacted the Loughborough-based researcher because, he says, “it occurred to me to model the behavior of a fluid passing through a porous medium with different levels of permeability, as in air purifiers. To do this, I proposed to study the coupling of the Brinkman-Forchheimer and Darcy equations, and I contacted Marco to help me formulate the transmission equations and provide physical support for the proposed model”. From this new collaboration, in 2023, came another publication, this time in Applied Numerical Mathematics.
“During the research visit, I focused on studying and learning the numerical technique of non-overlapping domain decomposition, with the aim of applying it to the problem we previously proposed and analyzed with Marco, and which was published in 2023,” detailed Caucao and commented that the objectives defined for the stay were amply met.
“We were able to propose a numerical scheme that allows decoupling the Brinkman-Forchheimer and Darcy problems, thus reducing the computational cost of solving them, since we work with two systems of smaller equations instead of a coupled system,” he said, adding that ‘another advantage of this numerical technique is that, computationally, it is easier to implement the problem in 3D’.
The funding for Caucao’s stay in the UK came entirely from funds committed by UCSC for the execution of the CMM basal project (FB210005).
By Iván R. Tobar Bocaz, journalist of the Center for Mathematical Modeling, Concepción.
Posted on Nov 22, 2024 in News
