On the stability of the symmetric interior penalty method for the Spalart-Allmaras turbulence model

Authors:
M. Drosson;K. Hillewaert
Affiliations:
Aerospace and Mechanical Department, University of Liège, Chemin des Chevreuils, 1, 4000 Liège, Belgium;Cenaero, CFD and Multiphysics Group, Rue des Frères Wright, 29, 6041 Gosselies, Belgium
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

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Abstract

The stability and convergence of the interior penalty (IP) discontinuous Galerkin method are closely related to the penalty coefficient @s"f. Using sharp trace inequalities adapted to the functional space, Shahbazi (2005) [7] has derived optimal values of @s"f for constant diffusivity problems on triangular meshes. We propose a generalisation of his analysis to account for mesh anisotropy and different element types on the one hand, and strong variations of the diffusivity on the other, which characterise the Spalart-Allmaras RANS turbulence model. The adequacy of this new definition is illustrated by applications to benchmark 2D computations. Finally, a comparison with two state of the art finite volume solvers is presented for a 3D high-lift cascade flow.