Abstract:
|
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. |