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The streamline upwind Petrov-Galerkin stabilising method for the numerical solution of highly advective problems
Implementación del método de estabilización de Petrov-Galerkin en contracorriente para la solución numérica de problemas altamente advectivos
DOI:
https://doi.org/10.15446/ing.investig.v29n2.15166Keywords:
streamline upwind Petrov Galerkin, stabilisation, diffusion-advection (en)Petrov Galerkin en contracorriente, estabilización, difusión-advección (es)
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This article describes the streamline upwind Petrov-Galerkin (SUPG) method as being a stabilisation technique for resolving the diffusion-advection-reaction equation by finite elements. The first part of this article has a short analysis of the importance of this type of differential equation in modelling physical phenomena in multiple fields. A one-dimensional description of the SUPG method is then given to extend this basis to two and three dimensions. The outcome of a strongly advective and a high numerical complexity experiment is presented. The results show how the version of the implemented SUPG technique allowed stabilised approaches in space, even for high Peclet numbers. Additional graphs of the numerical experiments presented here can be downloaded from www.gnum.unal.edu.co.
El presente artículo describe el método Petrov-Galerkin en contracorriente (SUPG) como técnica de estabilización de las soluciones por elementos finitos de la ecuación diferencial de difusión –advección- reacción. En la primera parte del artículo se hace un breve análisis de la importancia de este tipo de ecuaciones diferenciales para el modelado de fenómenos físicos en múltiples campos. Posteriormente, se realiza una descripción unidimensional del método SUPG y se desarrolla la metodología para implementar la técnica en dos o tres dimensiones. Se presentan los resultados de un experimento numérico fuertemente advéctico y de elevada complejidad desde el punto de vista numérico. Los resultados muestran cómo la versión de la técnica SUPG implementada permite aproximaciones estabilizadas en el espacio, aun para altos números de Peclet. Gráficas adicionales de los experimentos numéricos aquí presentados pueden ser descargados de www.gnum.unal.edu.co.
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Copyright (c) 2009 Carlos Humberto Galeano Urueña, Juan Miguel Mantilla González, Diego Alexander Garzón Alvarado
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