Algorithmes d'adaptation de maillages anisotropes et application à l'aérodynamique

The goal of this thesis is to study an anisotropic adaptive algorithm for transonic compressible viscous flow around an airwing. A convection-diffusion model problem is considered, an anisotropic a posteriori error estimator for the H1 semi-norm of the error is derived. The equivalence between the error and the estimator is proved, which provides the efficiency and the reliability of this estimator. A goal oriented anisotropic a posteriori error estimator is introduced. The equivalence with the error is not proved but lower and upper bounds are obtained. Based on this error estimator, an anisotropic mesh algorithm is proposed and applied to the transonic compressible flow around an airwing. The mesh is structured close to the boundary layer and is kept as is, while the mesh outside the boundary layer is adapted according to the anisotropic error estimator. This anisotropic adaptive algorithm allows shocks to be captured accurately, while keeping the number of vertices as low as possible.