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

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=107) are given and compared with benchmark solutions. Good accuracy is obtained with relatively coarse grids.
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https://hal.archives-ouvertes.fr/hal-01972136
Contributor : Frédéric Hecht <>
Submitted on : Monday, January 7, 2019 - 3:14:34 PM
Last modification on : Friday, May 24, 2019 - 5:00:23 PM

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Tomas Chacon Rebollo, Macarena Gómez Marmol, Frédéric Hecht, Samuele Rubino, Isabel Sánchez Muñoz. A High-Order Local Projection Stabilization Method for Natural Convection Problems. Journal of Scientific Computing, Springer Verlag, 2018, 74 (2), pp.667-692. ⟨10.1007/s10915-017-0469-9⟩. ⟨hal-01972136⟩

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