The aim of this work is to present a model reduction technique in the framework of optimal control problems for partial differential equations. We combine two approaches used for reducing the computational cost of the mathematical numerical models: domain–decomposition (DD) methods and reduced–order modelling (ROM). In particular, we consider an optimisation–based domain–decomposition algorithm for the parameter–dependent stationary incompressible Navier–Stokes equations. Firstly, the problem is described on the subdomains coupled at the interface and solved through an optimal control problem, which leads to the complete separation of the subdomain problems in the DD method. On top of that, a reduced model for the obtained optimal–control problem is built; the procedure is based on the Proper Orthogonal Decomposition technique and a further Galerkin projection. The presented methodology is tested on two fluid dynamics benchmarks: the stationary backward–facing step and lid-driven cavity flow. The numerical tests show a significant reduction of the computational costs in terms of both the problem dimensions and the number of optimisation iterations in the domain–decomposition algorithm.

An optimisation–based domain–decomposition reduced order model for the incompressible Navier-Stokes equations / Prusak, I.; Nonino, M.; Torlo, D.; Ballarin, F.; Rozza, G.. - In: COMPUTERS & MATHEMATICS WITH APPLICATIONS. - ISSN 0898-1221. - 151:(2023), pp. 172-189. [10.1016/j.camwa.2023.09.039]

An optimisation–based domain–decomposition reduced order model for the incompressible Navier-Stokes equations

Torlo D.;Rozza G.
2023

Abstract

The aim of this work is to present a model reduction technique in the framework of optimal control problems for partial differential equations. We combine two approaches used for reducing the computational cost of the mathematical numerical models: domain–decomposition (DD) methods and reduced–order modelling (ROM). In particular, we consider an optimisation–based domain–decomposition algorithm for the parameter–dependent stationary incompressible Navier–Stokes equations. Firstly, the problem is described on the subdomains coupled at the interface and solved through an optimal control problem, which leads to the complete separation of the subdomain problems in the DD method. On top of that, a reduced model for the obtained optimal–control problem is built; the procedure is based on the Proper Orthogonal Decomposition technique and a further Galerkin projection. The presented methodology is tested on two fluid dynamics benchmarks: the stationary backward–facing step and lid-driven cavity flow. The numerical tests show a significant reduction of the computational costs in terms of both the problem dimensions and the number of optimisation iterations in the domain–decomposition algorithm.
2023
Computational fluid dynamics; Domain decomposition; optimal control; proper orthogonal decomposition; reduced order modelling
01 Pubblicazione su rivista::01a Articolo in rivista
An optimisation–based domain–decomposition reduced order model for the incompressible Navier-Stokes equations / Prusak, I.; Nonino, M.; Torlo, D.; Ballarin, F.; Rozza, G.. - In: COMPUTERS & MATHEMATICS WITH APPLICATIONS. - ISSN 0898-1221. - 151:(2023), pp. 172-189. [10.1016/j.camwa.2023.09.039]
File allegati a questo prodotto
File Dimensione Formato  
Prusak_An-optimisation–based_2023.pdf

solo gestori archivio

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 4.05 MB
Formato Adobe PDF
4.05 MB Adobe PDF   Contatta l'autore
Prusak_postprint_An-optimisation–based_2023.pdf

accesso aperto

Tipologia: Documento in Post-print (versione successiva alla peer review e accettata per la pubblicazione)
Licenza: Creative commons
Dimensione 6.83 MB
Formato Adobe PDF
6.83 MB Adobe PDF

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1707515
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 3
social impact