Numerical Analysis of a Subgrid Scale Eddy Viscosity Method for Higher Reynolds Number Flow Problems

We develop a variationally consistent eddy viscosity model, given by [18] for convection diffusion equation, for the Navier-Stokes equations. We also prove that the new model is equivalent to a variational multiscale method. The new method removes the restriction that the fluctuations are quasi-stationary. We then give a complete error analysis. The error analysis is optimal and uniform in Reynolds number in all terms except for those arising from the reaction term in the linearized error equation. In particular, we show that error in the method for the Oseen problem is uniform in the Reynolds number.