In this work, we address parametric non-stationary fluid dynamics problems within a model order reduction setting based on domain decomposition. Starting from the domain decomposition approach, we derive an optimal control problem, for which we present the convergence analysis. The snapshots for the high-fidelity model are obtained with the Finite Element discretisation, and the model order reduction is then proposed both in terms of time and physical parameters, with a standard POD-Galerkin projection. We test the proposed methodology on two fluid dynamics benchmarks: the non-stationary backward-facing step and lid-driven cavity flow. Finally, also in view of future works, we compare the intrusive POD--Galerkin approach with a non--intrusive approach based on Neural Networks.

翻译：本文在基于区域分解的模型降阶框架下，研究了参数依赖的非定常流体动力学问题。从区域分解方法出发，我们推导出一个最优控制问题，并给出了其收敛性分析。高保真模型的快照通过有限元离散获得，随后在时间和物理参数两个维度上，采用标准的POD-Galerkin投影方法进行模型降阶。我们通过两个流体动力学基准算例检验了所提出的方法：非定常后向台阶流动和顶盖驱动空腔流动。最后，为便于未来研究，我们比较了侵入式POD-Galerkin方法与基于神经网络的非侵入式方法。