Direct simulations of the incompressible Navier-Stokes equations 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 regularizations of the non-linear convective term are examples thereof. In the present work, we propose a natural blending between both approaches: restoring the Galilean invariance of the regularization method leads to an additional hyper-viscosity term that can be viewed as a LES model. Technical details such as the determination of the filter length and the balancing between regularization and LES are analyzed and discussed. Finally, the performance of the method is assessed through application to the Burgers’ equation and a homogeneous isotropic turbulence.

Peer Reviewed