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 discretize the problem with the finite element method and we compare different model order reduction techniques: POD-Galerkin and a non-intrusive neural network procedure. 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.

翻译：本文针对模型降阶框架下基于区域分解的参数化非定常流体动力学问题进行研究。从基于优化的区域分解方法出发，推导出一个最优控制问题，针对非定常不可压缩Navier-Stokes方程给出了收敛性分析。采用有限元方法对问题进行离散化，并比较了不同的模型降阶技术：POD-Galerkin方法与非侵入式神经网络过程。结果表明，经典的POD-Galerkin方法在瞬态区域具有更强的鲁棒性和准确性，而神经网络方法虽能在存有时间或参数域不连续性时快速获得仿真结果但精度较低。我们在两个含物理参数和时间依赖性的流体动力学基准问题（非定常后向台阶流和顶盖驱动方腔流）上验证了所提方法的有效性。