A Reduced Basis LES turbulence model based upon Kolmogorov's equilibrium turbulence theory

In this work, we introduce an a posteriori error indicator for the reduced basis modelling of turbulent flows. It is based upon the $k^{-5/3}$ Kolmogorov turbulence theory, thus it may be applied to any numerical discretisation of LES turbulence models. The main idea of this indicator is that if the full-order solution and the Reduced Order solution are close enough, then their flow energy spectrum within the inertial range should also be close. We present some numerical tests which supports that the use of this indicator is helpful, obtaining large computational speed-ups. We use as full-order model a Finite Element discretisation of the unsteady LES Smagorinsky turbulence model.