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The incompressible Navier-Stokes equations constitute an excellent mathematical modelization of turbulence. Unfortunately, attempts at performing direct simulations 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 Simulation (LES) is an example thereof: they rely on differential operators that should be able to capture well different flow configurations (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.
Author(s):
F.Xavier Trias
Technical University of Catalonia
Spain
Roel Verstappen
University of Groningen
Netherlands
Andrey Gorobets
Technical University of Catalonia
Spain
Assensi Oliva
Technical University of Catalonia
Spain