A stable Spectral Difference approach for computations with triangular and hybrid grids up to the 6 th 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. Compared to the literature on the Spectral Difference approach, the present work outperforms published results in the order of accuracy that the stable formulation can deal with (p = 4 and p = 5). Moreover, the present approach differs with today reference approach called Flux Reconstruction method on hybrid grids. The proposed scheme is based on a set of flux points that are defined in the paper. The sets of point leading to a stable formulation are determined using a linear stability analysis. Two techniques are introduced, based on an optimization process or using published cubature points. For each order of accuracy, different sets of points lead to stable Spectral Difference schemes using Raviart-Thomas elements. Validation starts from the linear advection equation and ends with the laminar subsonic and transonic Navier-Stokes solutions over the NACA0012 airfoil using high order triangles and the laminar flow around a cylinder using a hybrid grid.

Mots clés: high-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 6 th order of accuracy. 2020. ⟨hal-02933792v1⟩