Analysis and development of subgrid turbulence models preserving the symmetry properties of the Navier–Stokes equations

Navier–Stokes equations have fundamental properties such as the invariance under some transformations, called symmetries, which play an important role in the description of the physics of the equations (conservation laws, wall laws, …). It is essential that turbulence models do not violate these properties. An analysis of a large set of subgrid models, according to the respect of the symmetries of Navier–Stokes equations is then done. As this analysis reveals that only few of the existing models are consistent with the symmetries, a new class of compatible models is proposed. This class is refined such that the models also respect the second law of thermodynamics. Finally, it is shown that this thermodynamic requirement leads to the stability of the model.