Error analysis of a residual-based stabilization-motivated POD-ROM for incompressible flows

This article presents error bounds for a velocity-pressure segregated POD reduced order model discretization of the Navier-Stokes equations. The stability is proven in L-infinity(L-2) and energy norms for velocity, with bounds that do not depend on the viscosity, while for pressure it is proven in a semi-norm of the same asymptotic order as the L-2 norm with respect to the mesh size. The proposed estimates are calculated for the two flow problems, the flow past a cylinder and the lid-driven cavity flow. Their quality is then assessed in terms of the predicted logarithmic slope with respect to the velocity POD contribution ratio. We show that the proposed error estimates allow a good approximation of the real errors slopes and thus a good prediction of their rate of convergence. (c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This article presents error bounds for a velocity-pressure segregated POD reduced order model discretization of the Navier-Stokes equations. The proposed estimates are proven to be stable and accurately predict the convergence rate of the real errors. The method is assessed using two flow problems and shows good predictive performance.