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In this work, we address parametric non-stationary fluid dynamics problemswithin a model order reduction setting based on domain decomposition. Startingfrom the domain decomposition approach, we derive an optimal control problem,for which we present the convergence analysis. The snapshots for thehigh-fidelity model are obtained with the Finite Element discretisation, andthe model order reduction is then proposed both in terms of time and physicalparameters, with a standard POD-Galerkin projection. We test the proposedmethodology on two fluid dynamics benchmarks: the non-stationarybackward-facing step and lid-driven cavity flow. Finally, also in view offuture works, we compare the intrusive POD--Galerkin approach with anon--intrusive approach based on Neural Networks.

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