Discontinuous Galerkin finite element discretization of a strongly anisotropic diffusion operator

Authors

  • A. Pestiaux,

    Corresponding author
    1. Earth and Life Institute (ELI), Georges Lemaître Centre for Earth and Climate Research (TECLIM), Université catholique de Louvain, Bte L4.03.08, place Louis Pasteur 3, B-1348 Louvain-la-Neuve, Belgium
    • Correspondence to: A. Pestiaux, Université catholique de Louvain, Earth and Life Institute (ELI), Georges Lemaître Centre for Earth and Climate Research (TECLIM), Bte L4.03.08, place Louis Pasteur 3, B-1348 Louvain-la-Neuve, Belgium.

      E-mail: alice.pestiaux@uclouvain.be

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  • S.A. Melchior,

    1. Institute of Mechanics, Materials and Civil Engineering (IMMC), Université catholique de Louvain, Bte L4.05.02, 4 avenue Georges Lemaître, B-1348 Louvain-la-Neuve, Belgium
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  • J.F. Remacle,

    1. Institute of Mechanics, Materials and Civil Engineering (IMMC), Université catholique de Louvain, Bte L4.05.02, 4 avenue Georges Lemaître, B-1348 Louvain-la-Neuve, Belgium
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  • T. Kärnä,

    1. Science and Technology Center for Coastal Margin Observation & Prediction, Institute of Environmental Health, Oregon Health & Science University, 20000 NW Walker Road, Beaverton, OR 97006, USA
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  • T. Fichefet,

    1. Earth and Life Institute (ELI), Georges Lemaître Centre for Earth and Climate Research (TECLIM), Université catholique de Louvain, Bte L4.03.08, place Louis Pasteur 3, B-1348 Louvain-la-Neuve, Belgium
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  • J. Lambrechts

    1. Institute of Mechanics, Materials and Civil Engineering (IMMC), Université catholique de Louvain, Bte L4.05.02, 4 avenue Georges Lemaître, B-1348 Louvain-la-Neuve, Belgium
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SUMMARY

The discretization of a diffusion equation with a strong anisotropy by a discontinuous Galerkin finite element method is investigated. This diffusion term is implemented in the tracer equation of an ocean model, thanks to a symmetric tensor that is composed of diapycnal and isopycnal diffusions. The strong anisotropy comes from the difference of magnitude order between both diffusions. As the ocean model uses interior penalty terms to ensure numerical stability, a new penalty factor is required in order to correctly deal with the anisotropy of this diffusion. Two penalty factors from the literature are improved and established from the coercivity property. One of them takes into account the diffusion in the direction normal to the interface between the elements. After comparison, the latter is better because the spurious numerical diffusion is weaker than with the penalty factor proposed in the literature. It is computed with a transformed coordinate system in which the diffusivity tensor is diagonal, using its eigenvalue decomposition. Furthermore, this numerical scheme is validated with the method of manufactured solutions. It is finally applied to simulate the evolution of temperature and salinity due to turbulent processes in an idealized Arctic Ocean. Copyright © 2014 John Wiley & Sons, Ltd.

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