This paper presents the construction of a correct-energy stabilized finite element method for the incompressible Navier-Stokes equations. The framework of the methodology and the correct-energy concept have been developed in the convective-diffusive context in the preceding paper [M.F.P. ten Eikelder, I. Akkerman, Correct energy evolution of stabilized formulations: The relation between VMS, SUPG and GLS via dynamic orthogonal small-scales and isogeometric analysis. I: The convective-diffusive context, Comput. Methods Appl. Mech. Engrg. 331 (2018) 259-280]. The current work extends ideas of the preceding paper to build a stabilized method within the variational multiscale (VMS) setting which displays correct-energy behavior. Similar to the convection-diffusion case, a key ingredient is the proper dynamic and orthogonal behavior of the small-scales. This is demanded for correct energy behavior and links the VMS framework to the streamline-upwind Petrov-Galerkin (SUPG) and the Galerkin/least-squares method (GLS).The presented method is a Galerkin/least-squares formulation with dynamic divergence-free small-scales (GLSDD). It is locally mass-conservative for both the large-and small-scales separately. In addition, it locally conserves linear and angular momentum. The computations require and employ NURBS-based isogeometric analysis for the spatial discretization. The resulting formulation numerically shows improved energy behavior for turbulent flows comparing with the original VMS method.

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