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An optimisation–based domain–decomposition reduced order model for parameter–dependent non–stationary fluid dynamics problems

TitleAn optimisation–based domain–decomposition reduced order model for parameter–dependent non–stationary fluid dynamics problems
Publication TypeJournal Article
Year of Publication2024
AuthorsPrusak, I, Torlo, D, Nonino, M, Rozza, G
JournalComputers & Mathematics with Applications
Volume166
Pagination253-268
ISSN0898-1221
KeywordsComputational fluid dynamics; Domain decomposition; Optimal control; POD–NN; Proper orthogonal decomposition; Reduced order modelling
Abstract

In this work, we address parametric non–stationary fluid dynamics problems within a model order reduction setting based on domain decomposition. Starting from the optimisation–based domain decomposition approach, we derive an optimal control problem, for which we present a convergence analysis in the case of non–stationary incompressible Navier–Stokes equations. We discretise the problem with the finite element method and we compare different model order reduction techniques: POD–Galerkin and a non–intrusive neural network procedures. We show that the classical POD–Galerkin is more robust and accurate also in transient areas, while the neural network can obtain simulations very quickly though being less precise in the presence of discontinuities in time or parameter domain. We test the proposed methodologies on two fluid dynamics benchmarks with physical parameters and time dependency: the non–stationary backward–facing step and lid–driven cavity flow.

URLhttps://www.sciencedirect.com/science/article/pii/S0898122124002098
DOI10.1016/j.camwa.2024.05.004

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