In this paper, a type of novel projection-based, time-segmented reduced order model (ROM) is proposed for dynamic fluid-structure interaction (FSI) problems based upon the arbitrary Lagrangian--Eulerian (ALE)-finite element method (FEM) in a monolithic frame, where spatially, each variable is separated from others in terms of their attribution (fluid/structure), category (velocity/pressure) and component (horizontal/vertical) while temporally, the proper orthogonal decomposition (POD) bases are constructed in some deliberately partitioned time segments tailored through extensive numerical trials. By the combination of spatial and temporal decompositions, the developed ROM approach enables prolonged simulations under prescribed accuracy thresholds. Numerical experiments are carried out to compare numerical performances of the proposed ROM with corresponding full-order model (FOM) by solving a two-dimensional FSI benchmark problem that involves a vibrating elastic beam in the fluid, where the performance of offline ROM on perturbed physical parameters in the online phase is investigated as well. Extensive numerical results demonstrate that the proposed ROM has a comparable accuracy to while much higher efficiency than the FOM. The developed ROM approach is dimension-independent and can be seamlessly extended to solve high dimensional FSI problems.

翻译：本文针对动态流固耦合问题，基于任意拉格朗日-欧拉有限元法的整体框架，提出了一种新型的基于投影的时间分段降阶模型。在空间上，各变量根据其属性（流体/固体）、类别（速度/压力）和分量（水平/垂直）相互分离；在时间上，通过大量数值试验精心划分时段，并在这些时段内构建本征正交分解基函数。通过结合空间和时间分解，所提出的降阶模型方法能够在预设精度阈值下实现长时间仿真。通过求解一个涉及流体中弹性梁振动的二维流固耦合基准问题，开展了数值实验，以比较所提降阶模型与相应全阶模型的数值性能，同时考察了离线降阶模型在在线阶段对扰动物理参数的性能。大量数值结果表明，所提降阶模型在保持与全阶模型相当精度的同时，具有更高的计算效率。该降阶模型方法具有维度无关性，可无缝扩展至求解高维流固耦合问题。