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A High-Order Local Projection Stabilization Method for Natural Convection Problems

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Abstract

In this paper, we propose a local projection stabilization (LPS) finite element method applied to numerically solve natural convection problems. This method replaces the projection-stabilized structure of standard LPS methods by an interpolation-stabilized structure, which only acts on the high frequencies components of the flow. This approach gives rise to a method which may be cast in the variational multi-scale framework, and constitutes a low-cost, accurate solver (of optimal error order) for incompressible flows, despite being only weakly consistent. Numerical simulations and results for the buoyancy-driven airflow in a square cavity with differentially heated side walls at high Rayleigh numbers (up to \(Ra=10^7\)) are given and compared with benchmark solutions. Good accuracy is obtained with relatively coarse grids.

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Acknowledgements

Research partially supported by Junta de Andalucía Excellence Project P12-FQM-454. Samuele Rubino would also gratefully acknowledge the financial support received from ERC Project H2020-EU.1.1.-639227, IdEx Bordeaux (Excellence Initiative of Université de Bordeaux) and FSMP (Fondation Sciences Mathématiques de Paris) during his postdoctoral research involved in this article.

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Authors and Affiliations

  1. Departamento EDAN and IMUS, Universidad de Sevilla, Sevilla, Spain

    Tomás Chacón Rebollo

  2. Departamento EDAN, Universidad de Sevilla, Sevilla, Spain

    Macarena Gómez Mármol

  3. Laboratoire Jacques-Louis Lions, Université Paris VI, Paris, France

    Frédéric Hecht

  4. Laboratoire I2M, IPB (UMR CNRS 5295), Université de Bordeaux, Talence, France

    Samuele Rubino

  5. Departamento Matemática Aplicada I, Universidad de Sevilla, Sevilla, Spain

    Isabel Sánchez Muñoz

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  1. Tomás Chacón Rebollo
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  2. Macarena Gómez Mármol
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  3. Frédéric Hecht
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  4. Samuele Rubino
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  5. Isabel Sánchez Muñoz
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Correspondence to Isabel Sánchez Muñoz.

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Chacón Rebollo, T., Gómez Mármol, M., Hecht, F. et al. A High-Order Local Projection Stabilization Method for Natural Convection Problems. J Sci Comput 74, 667–692 (2018). https://doi.org/10.1007/s10915-017-0469-9

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