We present a component-based model order reduction procedure to efficiently and accurately solve parameterized incompressible flows governed by the Navier-Stokes equations. Our approach leverages a non-overlapping optimization-based domain decomposition technique to determine the control variable that minimizes jumps across the interfaces between sub-domains. To solve the resulting constrained optimization problem, we propose both Gauss-Newton and sequential quadratic programming methods, which effectively transform the constrained problem into an unconstrained formulation. Furthermore, we integrate model order reduction techniques into the optimization framework, to speed up computations. In particular, we incorporate localized training and adaptive enrichment to reduce the burden associated with the training of the local reduced-order models. Numerical results are presented to demonstrate the validity and effectiveness of the overall methodology.

翻译：我们提出了一种基于组件的模型降阶流程，以高效且精确地求解由Navier-Stokes方程控制的参数化不可压缩流。该方法利用基于优化的非重叠区域分解技术，确定能够最小化子域间界面跳跃量的控制变量。为求解由此产生的约束优化问题，我们提出了高斯-牛顿法和序列二次规划法，这两种方法能有效将约束问题转化为无约束形式。此外，我们将模型降阶技术集成到优化框架中，以加速计算。具体而言，我们采用了局部训练与自适应扩充策略，以减轻局部降阶模型训练的计算负担。数值结果验证了整体方法的有效性与可靠性。