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Journal of Scientific Computing

, Volume 74, Issue 2, pp 667–692 | Cite as

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

  • Tomás Chacón Rebollo
  • Macarena Gómez Mármol
  • Frédéric Hecht
  • Samuele Rubino
  • Isabel Sánchez Muñoz
Article

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.

Keywords

Boussinesq equations Thermally coupled flows Natural convection LPS methods Finite elements Numerical analysis High Rayleigh number flows 

Notes

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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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Tomás Chacón Rebollo
    • 1
  • Macarena Gómez Mármol
    • 2
  • Frédéric Hecht
    • 3
  • Samuele Rubino
    • 4
  • Isabel Sánchez Muñoz
    • 5
  1. 1.Departamento EDAN and IMUSUniversidad de SevillaSevillaSpain
  2. 2.Departamento EDANUniversidad de SevillaSevillaSpain
  3. 3.Laboratoire Jacques-Louis LionsUniversité Paris VIParisFrance
  4. 4.Laboratoire I2M, IPB (UMR CNRS 5295)Université de BordeauxTalenceFrance
  5. 5.Departamento Matemática Aplicada IUniversidad de SevillaSevillaSpain

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