Adaptive anisotropic meshing for incompressible navier stokes using a VMS solver with boundary layer

Abstract : In this work, we propose to show that adaptive anisotropic meshing based on a posteriori estimation can be addressed for incompressible Navier Stokes at High Reynolds number. The proposed a posteriori estimate is based on the length distribution tensor approach and the associated edge based error analysis. It will be shown that boundary layer can be produced automatically on an unstructured mesh basis. The Finite Element flow solver is based on a Variational MultiScale (VMS) method, which consists in here of decomposition for both the velocity and the pressure fields into coarse/resolved scales and fine/unresolved scales. This choice of decomposition is shown to be favourable for simulating flows at high Reynolds number. The stabilization parameters are determined rigorously taking into account the anisotropy of the mesh using a directional element diameter.