On a certified VMS-Smagorinsky reduced basis model with LPS pressure stabilisation

In this work we introduce a certified Reduced Basis VMS-Smagorinsky turbulence model with local projection stabilisation (LPS) on the pressure, for steady state problems. We prove its stability for Taylor-Hood discretisations of velocity-pressure or piecewise linear pressure. We construct an a posteriori error estimator for the snapshot selection with 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. (c) 2022 IMACS. Published by Elsevier B.V. All rights reserved.