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

• Published in: Computers & mathematics with applications (1987) Vol. 166; pp. 253 - 268
• Main Authors: Prusak, Ivan, Torlo, Davide, Nonino, Monica, Rozza, Gianluigi
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 15.07.2024
• Subjects: Computational fluid dynamics; Domain decomposition; Optimal control; POD–NN; Proper orthogonal decomposition; Reduced order modelling; Reduced order modelling; Proper orthogonal decomposition; POD–NN; Computational fluid dynamics; Domain decomposition; Optimal control
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/j.camwa.2024.05.004

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. •Optimisation-based domain-decomposition algorithm for non-stationary computational fluid dynamics.•Convergence analysis for the domain-decomposition optimal control problem.•Comparison of the intrusive POD-Galerkin and a non-intrusive Neural Networks based approaches.