Article
Error analysis of a residual-based stabilization-motivated POD-ROM for incompressible flows
Author/s | Chacón Rebollo, Tomás
Rubino, Samuele Oulghelou, Mourad Allery, Cyrille |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2022-08-30 |
Deposit Date | 2024-01-25 |
Published in |
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Abstract | This article presents error bounds for a velocity–pressure segregated POD reduced order model discretization of the Navier–Stokes equations. The stability is proven in L∞(L2) and energy norms for velocity, with bounds that ... This article presents error bounds for a velocity–pressure segregated POD reduced order model discretization of the Navier–Stokes equations. The stability is proven in L∞(L2) and energy norms for velocity, with bounds that do not depend on the viscosity, while for pressure it is proven in a semi-norm of the same asymptotic order as the L2 norm with respect to the mesh size. The proposed estimates are calculated for the two flow problems, the flow past a cylinder and the lid-driven cavity flow. Their quality is then assessed in terms of the predicted logarithmic slope with respect to the velocity POD contribution ratio. We show that the proposed error estimates allow a good approximation of the real errors slopes and thus a good prediction of their rate of convergence. |
Funding agencies | Ministerio de Ciencia, Innovación y Universidades (MICIN). España |
Project ID. | RTI2018-093521-B-C31 |
Citation | Chacón Rebollo, T., Rubino, S., Oulghelou, M. y Allery, C. (2022). Error analysis of a residual-based stabilization-motivated POD-ROM for incompressible flows. Computer Methods in Applied Mechanics and Engineering, 401 (Part B), 115627-1. https://doi.org/10.1016/j.cma.2022.115627. |
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