The interest on embedded boundary methods is increasing in Computational Fluid Dynamics because they simplify the mesh generation problem when dealing with the Navier-Stokes equations. To give a few examples, they simplify the simulation of multi-physics flows, the coupling of fluid-solid interactions in situation of large motions or deformations. Nevertheless an accurate treatment of the wall boundary conditions remains an issue of the method. In this work, a penalty term added to the Navier-Stokes equations accounts for the wall boundary conditions and accuracy is recovered using mesh adaptation, thanks to the potential of unstructured meshes.