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Discontinuous Galerkin finite element discretization of a strongly anisotropic diffusion operator
Pestiaux, A.; Melchior, S.A.; Remacle, J.-F.; Karna, T.; Fichefet, T.; Lambrechts, J. (2014). Discontinuous Galerkin finite element discretization of a strongly anisotropic diffusion operator. Int. J. Numer. Methods Fluids 75(5): 365-384. dx.doi.org/10.1002/fld.3900
In: International Journal for Numerical Methods in Fluids. Wiley Interscience: Chichester; New York. ISSN 0271-2091, more
Peer reviewed article  

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Keyword
    Marine
Author keywords
    advection-diffusion; discontinuous Galerkin; interior penalty factor

Authors  Top 
  • Pestiaux, A., more
  • Melchior, S.A., more
  • Remacle, J.-F., more
  • Karna, T.
  • Fichefet, T., more
  • Lambrechts, J., more

Abstract
    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.

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