Analysis of a variational multiscale method for Large–Eddy simulation and its application to homogeneous isotropic turbulence

In this paper a variational multiscale method based on local projection and grad–div stabilization for Large–Eddy simulation for the incompressible Navier–Stokes problem is considered. An a priori error estimate is given for a case with rather general nonlinear (piecewise constant) coefficients of the subgrid models for the unresolved scales of velocity and pressure. Then the design of the subgrid scale models is specified for the case of homogeneous isotropic turbulence and studied for the standard benchmark problem of decaying homogeneous isotropic turbulence.