As we know that most LES codes(if not all) are based on the velocity-pressure description of Navier-Stokes equations. Is it possible that such a code could be based on the vorticity-velocity description, i.e. vorticity transport equation plus the definition of vorticity? What are the difficulties in doing so? Thanks.

There are no difficulties. In fact, since vorticity is the flow characteristic we are interested in most for turbulent flows, it only makes sense that we look at the velocity-vorticity formulation (at least for incompressible flow). I have posted in the past the significant advantages of this formulation over the traditional methods.

Anyway, the dynamic LES formulation for the vorticity-velocity based N-S has been presented in free space - no boundaries - for grid-free methods though there is nothing in the formulation that prevents one from using it for grid-based vorticity-velocity algorithms.

Check the following JCP papers:

Mansfield, Knio & Meneveau, A dynamic LES scheme for the vorticity transport equation: Formulation and a priori tests, JCP, vol 145, 693-730, 1998

Mansfield, Knio & Meneveau, Dynamic LES of colliding vortex rings using a 3D vortex method, JCP, vol 152, 305-345, 1999

Hope this helps

Adrin Gharakhani

Hi,

I guess that the problem is to define wall boundary condition for the vorticity.

Hi there,

Mansfield, JR et. al recently conducted the dynamic LES of colliding vortex rings using a 3D vortex method. (J. Comput. Phys. 152: 305~345 (1999). The solution is based on the vorticity-velocity discription which you may be interested in.

Hope this helps.

Tony