A stable Spectral Difference approach for computations with triangular and hybrid grids up to the 6th order of accuracy

Adèle Veilleux (1) , Guillaume Puigt (1) , Hugues Deniau (1) , Guillaume Daviller (2)

1 DMPE, ONERA, Université de Toulouse [Toulouse]
2 CERFACS - Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique

In the present paper, a stable spectral Difference formulation on triangles is defined using a flux polynomial expressed in the Raviart-Thomas basis up to the sixth-order of accuracy. Comparad to the literature on the Spectral Difference approach, the present work increases the order of accuracy that the stable formulation can deal with. The proposed scheme is bases on a set flux points defined in the paper. The sets of points leading to a stable formulation are determined using a Fourier stability analysis of the linear advection equation coupled with an optimization process. The proposed Spectral Difference formulation differs from the Flux Reconstruction method on hybrid grids: the distinction between the two approaches is highlighted through the definition of the number of interior flux points. Validation starts from over the NACA0012 airfoil using quadratic triangles and of the laminar flow around a cylinder using a hybrid grid.

Mots clés: Hgh-order method; Spectral Difference method; Triangle; Quadrangle; Linear stability analysis

Mots clés: Méthode d'ordre élevé; Méthode des différences spectrales; Triangle; Quadrangle; Analyse de stabilité linéaire

Domaines: Sciences de l'ingénieur [physics]; Physique [physics]

Adèle Veilleux, Guillaume Puigt, Hugues Deniau, Guillaume Daviller. A stable Spectral Difference approach for computations with triangular and hybrid grids up to the 6th order of accuracy. 2021. ⟨hal-02933792v2⟩