An anisotropic adaptive finite element algorithm for transonic viscous flows around a wing

• 3D anisotropic adaptive finite element algorithm to compute the transonic viscous flow around a wing.
• The adaptive criterion is justified through anisotropic a posteriori error estimates for an model problem.
• Numerical results for the model problem confirm the theoretical predictions.
• Numerical results with adaptive anisotropic meshes are compared to experimental ones for the ONERA M6 wing.

An adaptive finite element algorithm to compute transonic viscous flows around a wing is presented. The adaptive criteria is based on an anisotropic error estimator in the H1H1 semi-norm, justified for an advection–diffusion problem with stabilized finite elements. The mesh aspect ratio can be arbitrarily large, upper and lower bounds can be proved, the involved constants being aspect ratio independent.Based on this error estimator, an anisotropic mesh adaptation algorithm is proposed to compute transonic viscous flows around a wing. The mesh is structured around the wing, while the remaining part of the mesh is adapted according to the anisotropic error estimator. This anisotropic adaptive algorithm allows shocks and the wake to be captured accurately, while keeping the number of vertices as low as possible.