Solution of high-Reynolds incompressible flow with stabilized finite element and adaptive anisotropic meshing

The objective of this paper is to show that anisotropic meshes with highly stretched elements can be used to compute high Reynolds number flows. In particular, it will be shown that boundary layers, flow detachments and all vortices are well captured automatically by the mesh. We present an anisotropic meshing based on a posteriori estimation for the incompressible Navier Stokes equations. The proposed a posteriori estimate is based on the length distribution tensor approach and the associated edge based error analysis. The Finite Element flow solver is based on a Variational MultiScale (VMS) method, which consists in here of decomposing both the velocity and the pressure fields into coarse/resolved and fine/unresolved scales. This choice of decomposition is shown to be efficient for simulating flows at high Reynolds number. The stabilization parameters are determined taking into account the anisotropy of the mesh using a directional element diameter. The adaptation algorithm is applied to high Reynolds number flows inside the 2D and 3D lid-driven cavities and compared to accurate reference solutions.