Details

Autor(en) / Beteiligte

• Pestiaux, A.
• Melchior, S.A.
• Remacle, J.F.
• Kärnä, T.
• Fichefet, T.
• Lambrechts, J.

Titel

Discontinuous Galerkin finite element discretization of a strongly anisotropic diffusion operator

Ist Teil von

• International journal for numerical methods in fluids, 2014-06, Vol.75 (5), p.365-384

Ort / Verlag

Bognor Regis: Blackwell Publishing Ltd

Erscheinungsjahr

2014

Quelle

Wiley Online Library - AutoHoldings Journals

Beschreibungen/Notizen

• SUMMARYThe 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. In this paper, the discretization of a diffusion equation with a strong anisotropy by a discontinuous Galerkin finite element method is investigated. Two penalty factors from the literature have been improved and established from the coercivity property, in order to ensure stability and especially the efficiency of the system. The oriented penalty factor guarantees the weakest spurious numerical diffusion (right figure) and allows to have a well‐conditioned system. Finally, this factor is used in a physical application : an idealized Arctic Ocean.