Since direct numerical simulation (DNS) cannot be performed at high Reynolds number, a dynamically less complex mathematical formulation is sought. In the quest for such formulation, we consider regularization (smooth approximations) of the nonlinearity. The regularization method basically alters the convective terms to reduce the production of small scales of motion by means of vortex stretching. In doing so, we propose to preserve the symmetry and conservation properties of the convective terms exactly. This requirement yields a novel class of regularizations that restrain the convective production of smaller and smaller scales of motion by means of vortex stretching in an unconditional stable manner, meaning that the velocity can not blow up in the energy-norm (in 2D also: enstrophy-norm). The numerical algorithm used to solve the governing equations preserves the symmetry and conservation properties too. In the present work, regularization modelling is tested for a fully-3D geometry: turbulent flow around a wall-mounted cube at Reh = 7235 (based on the cube height and the bulk velocity). Modelled results are compared with the new DNS results carried out on the MareNostrum supercomputer using 300 CPU on a structured Cartesian mesh with ~ 16 × 10 6 points. The algorithm used to solve the Poisson equation works well on arbitrarily meshed 3D grids and is therefore well-suited for the proposed DNS simulation. Moreover, details about the Poisson solver for DNS and the parallelization of code are also discussed.

Peer Reviewed