Article
A cure for instabilities due to advection-dominance in POD solution to advection-diffusion-reaction equations
Author/s | Azaïez, Mejdi
Chacón Rebollo, Tomás Rubino, Samuele |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2021-01-15 |
Deposit Date | 2022-10-28 |
Published in |
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Abstract | In this paper, we propose to improve the stabilized POD-ROM introduced in [48] to deal with the numerical simulation of advection-dominated advection-diffusion-reaction equations. In particular, we propose a three-stage ... In this paper, we propose to improve the stabilized POD-ROM introduced in [48] to deal with the numerical simulation of advection-dominated advection-diffusion-reaction equations. In particular, we propose a three-stage stabilizing strategy that will be very useful when considering very low diffusion coefficients, i.e. in the strongly advection-dominated regime. This approach mainly consists in three ingredients: (1) the addition of a “streamline diffusion” stabilization term to the governing projected equations, (2) the modification of the correlation matrix defining the POD modes associated to the advection stabilization term, and (3) an a-posteriori stabilization scheme. Numerical studies are performed to discuss the accuracy and performance of the new method in handling strongly advection-dominated cases. |
Citation | Azaïez, M., Chacón Rebollo, T. y Rubino, S. (2021). A cure for instabilities due to advection-dominance in POD solution to advection-diffusion-reaction equations. Journal of Computational Physics, 425, 109916. https://doi.org/10.1016/j.jcp.2020.109916. |
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