A discretize-then-map approach for the treatment of parameterized geometries in model order reduction - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Computer Methods in Applied Mechanics and Engineering Année : 2021

A discretize-then-map approach for the treatment of parameterized geometries in model order reduction

Résumé

We propose a new general approach for the treatment of parameterized geometries in projection-based model order reduction. During the offline stage, given (i) a family of parameterized domains $\{ \Omega_{\mu}: \mu \in \mathcal{P} \} \subset \mathbb{R}^D$ where $\mu \in \mathcal{P} \subset \mathbb{R}^P$ denotes a vector of parameters, (ii) a parameterized mapping $\underline{\Phi}_{\mu}$ between a reference domain $\Omega$ and the parameter-dependent domain $\Omega_{\mu}$, and (iii) a finite element triangulation of $\Omega$, we resort to an empirical quadrature procedure to select a subset of the elements of the grid. During the online stage, we first use the mapping to "move" the nodes of the selected elements and then we use standard element-wise residual evaluation routines to evaluate the residual and possibly its Jacobian. We discuss how to devise an online-efficient reduced-order model and we discuss the differences with the more standard "map-then-discretize" approach (e.g., Rozza, Huynh, Patera, ACME, 2007); in particular, we show how the discretize-then-map framework greatly simplifies the implementation of the reduced-order model. We apply our approach to a two-dimensional potential flow problem past a parameterized airfoil, and to the two-dimensional RANS simulations of the flow past the Ahmed body.
Fichier principal
Vignette du fichier
S0045782521002930.pdf (1.25 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03120853 , version 1 (13-06-2023)

Licence

Identifiants

Citer

Tommaso Taddei, Lei Zhang. A discretize-then-map approach for the treatment of parameterized geometries in model order reduction. Computer Methods in Applied Mechanics and Engineering, 2021, ⟨10.1016/j.cma.2021.113956⟩. ⟨hal-03120853⟩
50 Consultations
10 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More