On a certified VMS-Smagorinsky Reduced Basis model with LPS pressure stabilisation

TL;DR

This paper introduces a certified Reduced Basis VMS-Smagorinsky turbulence model with LPS pressure stabilisation, providing stability proofs, an  posteriori error estimator, and demonstrating improved computational speed in numerical tests.

Contribution

It presents a novel certified Reduced Basis turbulence model with LPS pressure stabilisation, including stability proof, error estimation, and efficiency improvements over pressure supremizer methods.

Findings

Enhanced computational speed with LPS pressure stabilisation

Proven stability for Taylor-Hood discretisations

Effective  posteriori error estimation for snapshot selection

Abstract

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.