New Differential Operators and Discretization Methods for Eddy-viscosity Models for LES

The incompressible Navier-Stokes equations constitute an excellent mathematical modelization of turbulence. Unfortunately, at- tempts at performing direct numerical simulations (DNS) are limited to relatively low-Reynolds numbers. Therefore, dynamically less complex mathematical formulations are necessary for coarse-grain simulations. Eddy-viscosity models for Large-Eddy Sim- ulation (LES) is an example thereof: they rely on differential operators that should be able to capture well different flow config- urations (laminar and 2D flows, near-wall behavior, transitional regime...). In the present work, several differential operators are derived from the criterion that vortex-stretching mechanism must stop at the smallest grid scale. Moreover, since the discretization errors may play an important role a novel approach to discretize the viscous term with spatially varying eddy-viscosity is used. It is based on basic operators; therefore, the implementation is straightforward even for staggered formulations. The performance of the proposed models will be assessed by means of direct comparison to DNS reference results.