论文标题
基于优化的域分解降低了不可压缩的Navier-Stokes方程的订单模型
An optimisation-based domain-decomposition reduced order model for the incompressible Navier-Stokes equations
论文作者
论文摘要
这项工作的目的是在针对部分微分方程的最佳控制问题框架中介绍一种模型减少技术。我们结合了用于降低数学模型的计算成本的两种方法：域分解（DD）方法和还原阶建模（ROM）。特别是，我们考虑了一种基于优化的域分解算法，用于参数依赖性固定不可压缩的Navier-Stokes方程。首先，该问题在接口处耦合并通过最佳控制问题解决的子域进行了描述，从而导致DD方法中亚域问题的完全分离。最重要的是，为获得的最佳控制问题而减少了模型。该过程基于适当的正交分解技术和进一步的盖尔金投影。呈现的方法对两个流体动力学基准进行了测试：固定的向后步骤和盖子驱动的空腔流。数值测试表明，从问题维度和域分解算法中的优化迭代次数方面，计算成本显着降低。
The aim of this work is to present a model reduction technique in the framework of optimal control problems for partial differential equations. We combine two approaches used for reducing the computational cost of the mathematical numerical models: domain-decomposition (DD) methods and reduced-order modelling (ROM). In particular, we consider an optimisation-based domain-decomposition algorithm for the parameter-dependent stationary incompressible Navier-Stokes equations. Firstly, the problem is described on the subdomains coupled at the interface and solved through an optimal control problem, which leads to the complete separation of the subdomain problems in the DD method. On top of that, a reduced model for the obtained optimal-control problem is built; the procedure is based on the Proper Orthogonal Decomposition technique and a further Galerkin projection. The presented methodology is tested on two fluid dynamics benchmarks: the stationary backward-facing step and lid-driven cavity flow. The numerical tests show a significant reduction of the computational costs in terms of both the problem dimensions and the number of optimisation iterations in the domain-decomposition algorithm.
