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

The stability and convergence of the interior penalty (IP) discontinuous Galerkin method are closely related to the penalty coefficient σfσf. Using sharp trace inequalities adapted to the functional space, Shahbazi (2005) [7] has derived optimal values of σfσf 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.