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.

翻译：本文提出了一种用于湍流降阶基建模的后验误差指标。该指标基于$k^{-5/3}$ Kolmogorov湍流理论，因此可应用于任意LES湍流模型的数值离散格式。该指标的核心思想是：若全阶解与降阶解足够接近，则两者在惯性子区内的流动能量谱也应足够接近。我们通过若干数值实验验证了该指标的有效性，并获得了显著的计算加速比。本文采用非定常LES Smagorinsky湍流模型的有限元离散作为全阶模型。