In this work we introduce a certified Reduced Basis VMS-Smagorinsky turbulence model with local projection stabilisation (LPS) on the pressure. We prove its stability for Taylor-Hood discretisations of velocity-pressure. We construct an \textit{a posteriori} error estimator for the snapshot selection through a Greedy algorithm, based on the Brezzi-Rappaz-Raviart theory of approximation of non-singular branches of non-linear PDEs. The Empirical Interpolation Method (EIM) is used for the approximation of the non-linear terms. We present some numerical tests in which we show an improved speedup on the computation of the reduced basis problem with the LPS pressure stabilisation, with respect to the method of using pressure supremizers.

翻译：本文提出了一种具有局部投影稳定（LPS）压力项的认证化降阶基VMS-Smagorinsky湍流模型。我们证明了该模型在速度-压力Taylor-Hood离散格式下的稳定性。基于非线性偏微分方程非奇异分支逼近的Brezzi-Rappaz-Raviart理论，通过贪婪算法构建了用于快照选择的先验误差估计器。采用经验插值法（EIM）逼近非线性项。数值实验表明，与使用压力上确界算子的方法相比，本方法在带LPS压力稳定的降阶基问题求解中实现了更优的加速比。