This article presents a Galerkin projection model order reduction approach for fluid-structure interaction (FSI) problems in the Finite Volume context. The reduced-order model (ROM) is based on proper orthogonal decomposition (POD), where a reduced basis is formed using energy-dominant POD modes. The reduced basis also consists of characteristics of the POD time modes derived from the POD time modes coefficients. In addition, the solution state vector comprises the mesh deformation, considering the structural motion in FSI. The results are obtained by applying the proposed method to time-dependent problems governed by the 2D incompressible Navier-Stokes equations. The main objective of this work is to introduce a hybrid technique mixing up the classical Galerkin-projection approach with a data-driven method to obtain a versatile and accurate algorithm for resolving FSI problems with moving meshes. The effectiveness of this approach is demonstrated in the case study of vortex-induced vibrations (VIV) of a cylinder at Reynolds number Re = 200. The results show the stability and accuracy of the proposed method with respect to the high-dimensional model by capturing transient flow fields and, more importantly, the forces acting on the moving objects.

翻译：本文提出一种面向有限体积格式中流固耦合（FSI）问题的Galerkin投影模型降阶方法。该降阶模型基于本征正交分解（POD），通过能量主导的POD模态构建降阶基。降阶基还包含由POD时间模态系数导出的POD时间模态特征。此外，解状态向量包含考虑FSI中结构运动的网格变形。通过将所提方法应用于二维不可压缩Navier-Stokes方程控制的时间相关问题获得计算结果。本研究的主要目标是引入一种混合技术，将经典Galerkin投影方法与数据驱动方法相结合，以构建一种适用于动网格FSI问题的通用且精确的算法。以雷诺数Re=200圆柱涡激振动（VIV）为案例验证该方法有效性。结果表明，所提方法在捕捉瞬态流场及运动物体所受作用力方面，相较于高维模型展现出稳定性和准确性。