On the convergence of a fully discrete scheme of LES type to physically relevant solutions of the incompressible Navier–Stokes

Obtaining reliable numerical simulations of turbulent fluids is a challenging problem in computational fluid mechanics. The large eddy simulation (LES) models are efficient tools to approximate turbulent fluids, and an important step in the validation of these models is the ability to reproduce relevant properties of the flow. In this paper, we consider a fully discrete approximation of the Navier–Stokes–Voigt model by an implicit Euler algorithm (with respect to the time variable) and a Fourier–Galerkin method (in the space variables). We prove the convergence to weak solutions of the incompressible Navier–Stokes equations satisfying the natural local entropy condition, hence selecting the so-called physically relevant solutions.