The incompressible Navier-Stokes equations form an excellent mathematical model for turbulent flows. However, direct simulations at high Reynolds numbers are not feasible because the convective term produces far too many relevant scales of motion. Therefore, in the foreseeable future numerical simulations of turbulent flows will have to resort to models of the small scales. Large-eddy simulation (LES) and regularization models are examples thereof. In the present work, we propose to combine both approaches. Restoring the Galilean invariance of the regularization method results into an additional hyperviscosity term. This approach provides a natural blending between regularization and LES. The performance of these recent improvements will be assessed through application to homogeneous isotropic turbulence, a turbulent channel flow and a wind-farm turbulent boundary layer.

Peer Reviewed