This work is devoted to the development of efficient methods for the numerical simulation of incompressible flows on modern supercomputers. Direct simulation of the Navier-Stokes equations is nowadays an essential tool to provide new insights into the physics of turbulence and indispensable data for the development of better turbulence models. However, since DNS simulations at high Reynolds numbers are not feasible because the convective term produces far too many scales of motion, a dynamically less complex mathematical formulation is sought. In the quest for such a formulation, we consider regularizations of the convective term that preserve symmetry and conservation properties exactly. This yields a novel class of regularizations that restrain the convective production of small scales of motion in an unconditionally stable manner. In this way, the new set of equations is dynamically less complex than the original Navier-Stokes equations, and therefore more amenable to be numerically solved. The only additional ingredient is a self-adjoint linear filter whose local filter length is determined from the requirement that vortex-stretching must be stopped at the scale set by the grid. Here, the performance of the method is tested by means of direct comparison with several DNS reference simulations.

Peer Reviewed