Since direct numerical simulations cannot be computed at high Reynolds numbers, a dynamically less complex formulation is sought. In the quest for such a formulation, we consider regularizations of the convective term that preserve the symmetry and conservation properties exactly. This requirement yielded a novel class of regularizations (Computers & Fluids 37 (2008) 887) that restrain the convective production of smaller and smaller scales of motion in an unconditionally stable manner, meaning that the velocity cannot blow up in the energy-norm (in 2D also: enstrophy-norm). The numerical algorithm used to solve the governing equations must preserve the symmetry and conservation properties too. To do so, one of the most critical issues is the discrete filtering. The method requires a list of properties that, in general, are not preserved by classical filters for LES unless they are imposed a posteriori. In the present paper, we propose a novel class of discrete filters that preserves such properties per se. They are based on polynomial functions of the discrete diffusive operator, ˜D, with the general form F = I + PM m=1 dm ˜D m. Then, the coefficients, dm, follow from the requirement that, at the smallest grid scale kc, the amount by which the interactions between the wavevector-triples (kc, kc − q, q) are damped must become virtually independent of the q-th Fourier-mode. This allows an optimal control of the subtle balance between convection and diffusion at the smallest grid scale to stop the vortex-stretching. Finally, the proposed method is tested for an air-filled differentially heated cavity of height aspect ratio 4.

Peer Reviewed