Efecto del mallado en el aprendizaje de métodos variacionales: cuando la discretización afecta la interpretación

Cesar Pairetti

Authors

Cesar Pairetti Universidad Nacional de Rosario https://orcid.org/0009-0003-6159-0470

Abstract

Computational thinking has deeply transformed the way scientific problems are represented and solved. This paper analyzes how spatial discretization strategies influence the conceptual understanding of variational methods, which are key to the numerical resolution of partial differential equations. Through a comparative study of two widely used platforms –OpenFOAM and Basilisk– the work examines how their data structures model space and constrain the design of algorithms and differential operators, focusing on turbulence simulation as a representative case.

Drawing on the epistemological contributions of Piaget and García, the paper argues that these technical choices are not neutral: they shape specific ways of thinking about physical phenomena and validating solutions. It is argued that the differences between these numerical modeling paradigms should be considered not only when selecting computational tools but also when designing engineering curricula. Finally, based on the analysis presented, the paper offers a critical reflection on the impact of numerical tools –including large language models– on the cognitive development of future professionals. In a context of massive and often uncritical adoption of technologies based on discrete mathematics and statistics, it becomes crucial to reassess their epistemological implications.

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Author Biography

Cesar Pairetti, Universidad Nacional de Rosario

Es Profesor Adjunto en la Facultad de Ciencias Exactas, Ingeniería y Agrimensura de la Universidad Nacional de Rosario (UNR). Sus principales líneas de investigación se relacionan a la simulación numérica, especialmente a la dinámica de fluidos aplicada a problemas de atomización, transferencia de calor, flujo multifásico y cambios de fase. Por otra parte, colabora con el grupo de Dispositivos Intermediales Dinámicos (DID) del Instituto Rosario de Investigaciones en Ciencias de la Educación (IRICE) perteneciente al Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) y a la UNR, estudiando metodologías de enseñanza-aprendizaje en el contexto de carreras STEAM, atravesadas por el uso de TIC, más puntualmente de aplicaciones relacionadas con herramientas de inteligencia artificial.

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