Seminar by Tomás Chacón Rebollo

Speaker

Tomás Chacón Rebollo (Universidad de Sevilla)

Title

Some techniques for the stabilisation of the pressure discretization in Reduced Order Models of incompressible fluids

Date

  • February 07, 2023 16:00 CET+0100 (Europe/Rome)

  • February 07, 2023 10:00 EST-0500 (US/Eastern)

  • February 07, 2023 09:00 CST-0600 (US/Central)

  • February 07, 2023 07:00 PST-0800 (US/Pacific)

Abstract

In this talk we address the stability of the pressure discretisation for Reduced Order Models (ROMs) of incompressible flows. For Galerkin discretisations of incompressible fluids, the discrete inf-sup condition for the duality velocity - pressure gradient can be achieved to ROMs by adding velocity supremisers (the Riesz representation of the pressure gradient on the velocity space). However, it is rather costly and several alternative strategies can be carried on. Among them, stabilisation techniques or post-processing of the pressure. On one side we shall present several stabilisation procedures that ensure the well posedness of the reduced problem, in norms weaker than the \(L^2\) norm for the pressure. We apply this technique to the Reduced-Basis solution of the Smagorinsky turbulence model. On another hand we shall study a post-processing of the pressure from divergence-free POD-ROM velocity. We prove error estimates again in a norm weaker than the \(L^2\) for the pressure.

This is joint work with Cyrille Alléry, Enrique Delgado, Mourad Oulghelou and Samuele Rubino.

Recording

Watch the recording on our YouTube channel.